Thomas' Calculus: Early Transcendentals, Single Variable (14th Edition)
14th Edition
ISBN: 9780134439419
Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher: PEARSON
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Chapter 3.3, Problem 59E
To determine
Find the value of constants a, b, and c.
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4. Consider the initial value problem
y' = 3x(y-1) 1/3,
y(xo) = yo.
(a) For what points (co, yo) does the IVP have a solution?
(b) For what points (xo, yo) does the IVP have a unique solution on some open interval that contains 20?
(c) Solve the IVP
y' = 3x(y-1) 1/3,
y(0) = 9
and determine the largest open interval on which this solution is unique.
Find the limit. (If the limit is infinite, enter 'oo' or '-o', as appropriate. If the limit does not otherwise exist, enter DNE.)
lim
X→ ∞
(✓
81x2
-
81x + x
9x)
2) Compute the following anti-derivative.
√1x4 dx
Chapter 3 Solutions
Thomas' Calculus: Early Transcendentals, Single Variable (14th Edition)
Ch. 3.1 - In Exercises 1–4, use the grid and a straight edge...Ch. 3.1 - In Exercises 1-4, use the grid and a straight edge...Ch. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - In Exercises 510, find an equation for the tangent...Ch. 3.1 - In Exercises 510, find an equation for the tangent...Ch. 3.1 - In Exercises 510, find an equation for the tangent...Ch. 3.1 - In Exercises 510, find an equation for the tangent...Ch. 3.1 - Prob. 9ECh. 3.1 - In Exercises 510, find an equation for the tangent...
Ch. 3.1 - Prob. 11ECh. 3.1 - In Exercises 11–18, find the slope of the...Ch. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - In Exercises 19–22, find the slope of the curve at...Ch. 3.1 - In Exercises 19–22, find the slope of the curve at...Ch. 3.1 - In Exercises 19–22, find the slope of the curve at...Ch. 3.1 - Interpreting Derivative Values
Growth of yeast...Ch. 3.1 - Effectiveness of a drug On a scale from 0 to 1,...Ch. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Object dropped from a tower An object is dropped...Ch. 3.1 - Speed of a rocket At t sec after liftoff, the...Ch. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Find the slope of the tangent line to the curve y...Ch. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Prob. 40ECh. 3.1 - Prob. 41ECh. 3.1 - Prob. 42ECh. 3.1 - Prob. 43ECh. 3.1 - Prob. 44ECh. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - Prob. 47ECh. 3.1 - Graph the curves in Exercises 39–48.
Where do the...Ch. 3.2 - Using the definition, calculate the derivatives of...Ch. 3.2 - Using the definition, calculate the derivatives of...Ch. 3.2 - Using the definition, calculate the derivatives of...Ch. 3.2 - Prob. 4ECh. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - In Exercises 17–18, differentiate the functions....Ch. 3.2 - In Exercises 19–22, find the values of the...Ch. 3.2 - In Exercises 19–22, find the values of the...Ch. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Use the formula
to find the derivative of the...Ch. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Match the functions graphed in Exercises 27–30...Ch. 3.2 - Match the functions graphed in Exercises 27–30...Ch. 3.2 - Match the functions graphed in Exercises 27–30...Ch. 3.2 - Prob. 30ECh. 3.2 - Consider the function f graphed here. The domain...Ch. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Fruit flies (Continuation of Example 4, Section...Ch. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - Prob. 37ECh. 3.2 - Prob. 38ECh. 3.2 - Prob. 39ECh. 3.2 - Compute the right-hand and left-hand derivatives...Ch. 3.2 - In Exercises 41–44, determine whether the...Ch. 3.2 - In Exercises 41–44, determine whether the...Ch. 3.2 - In Exercises 41–44, determine whether the...Ch. 3.2 - Prob. 44ECh. 3.2 - Prob. 45ECh. 3.2 - Prob. 46ECh. 3.2 - Prob. 47ECh. 3.2 - Prob. 48ECh. 3.2 - Prob. 49ECh. 3.2 - Each figure in Exercises 45–50 shows the graph of...Ch. 3.2 - Prob. 51ECh. 3.2 - In Exercises 51–54,
Find the derivative f'(x) of...Ch. 3.2 - In Exercises 51–54,
Find the derivative f'(x) of...Ch. 3.2 - In Exercises 51–54,
Find the derivative f'(x) of...Ch. 3.2 - Tangent line to a parabola Does the parabola y =...Ch. 3.2 - Tangent line to Does any tangent line to the...Ch. 3.2 - Prob. 57ECh. 3.2 - Derivative of multiples Does knowing that a...Ch. 3.2 - Limit of a quotient Suppose that functions g(t)...Ch. 3.2 - Let f(x) be a function satisfying for . Show that...Ch. 3.2 - Prob. 61ECh. 3.2 - Prob. 62ECh. 3.2 - Prob. 63ECh. 3.2 - Prob. 64ECh. 3.3 - Derivative Calculations
In Exercises 112, find the...Ch. 3.3 - Derivative Calculations
In Exercises 112, find the...Ch. 3.3 - Derivative Calculations
In Exercises 112, find the...Ch. 3.3 - Derivative Calculations
In Exercises 112, find the...Ch. 3.3 - Derivative Calculations
In Exercises 112, find the...Ch. 3.3 - Derivative Calculations
In Exercises 112, find the...Ch. 3.3 - Derivative Calculations
In Exercises 112, find the...Ch. 3.3 - Derivative Calculations
In Exercises 112, find the...Ch. 3.3 - Derivative Calculations
In Exercises 112, find the...Ch. 3.3 - Derivative Calculations
In Exercises 112, find the...Ch. 3.3 - Derivative Calculations
In Exercises 112, find the...Ch. 3.3 - Derivative Calculations
In Exercises 112, find the...Ch. 3.3 - In Exercises 1316, find y'(a) by applying the...Ch. 3.3 - In Exercises 1316, find y' (a) by applying the...Ch. 3.3 - In Exercises 1316, find y' (a) by applying the...Ch. 3.3 - Prob. 16ECh. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Prob. 33ECh. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Prob. 40ECh. 3.3 - Find the derivatives of all orders of the...Ch. 3.3 - Find the derivatives of all orders of the...Ch. 3.3 - Prob. 43ECh. 3.3 - Prob. 44ECh. 3.3 - Prob. 45ECh. 3.3 - Find the first and second derivatives of the...Ch. 3.3 - Prob. 47ECh. 3.3 - Prob. 48ECh. 3.3 - Prob. 49ECh. 3.3 - Prob. 50ECh. 3.3 - Prob. 51ECh. 3.3 - Prob. 52ECh. 3.3 - Prob. 53ECh. 3.3 - Prob. 54ECh. 3.3 - Normal line to a curve Find an equation for the...Ch. 3.3 - Prob. 56ECh. 3.3 - Find the tangent lines to Newton’s serpentine...Ch. 3.3 - Find the tangent line to the Witch of Agnesi...Ch. 3.3 - Quadratic tangent to identity function The curve y...Ch. 3.3 - Prob. 60ECh. 3.3 - Find all points (x, y) on the graph of f(x) = 3x2...Ch. 3.3 - Find all points (x, y) on the graph of with...Ch. 3.3 - Find all points (x, y) on the graph of y = x/(x −...Ch. 3.3 - Find all points (x, y) on the graph of f(x) = x2...Ch. 3.3 - Assume that functions f and g are differentiable...Ch. 3.3 - Assume that functions f and g are differentiable...Ch. 3.3 - Find an equation for the line that is tangent to...Ch. 3.3 - Find an equation for the line that is tangent to...Ch. 3.3 - For Exercises 69 and 70, evaluate each limit by...Ch. 3.3 - For Exercises 69 and 70, evaluate each limit by...Ch. 3.3 - Prob. 71ECh. 3.3 - Prob. 72ECh. 3.3 - Prob. 73ECh. 3.3 - Prob. 74ECh. 3.3 - Prob. 75ECh. 3.3 - Prob. 76ECh. 3.3 - Generalizing the Product Rule The Derivative...Ch. 3.3 - Power Rule for negative integers Use the...Ch. 3.3 - Cylinder pressure If gas in a cylinder is...Ch. 3.3 - Prob. 80ECh. 3.4 - Exercises 1–6 give the positions s = f(t) of a...Ch. 3.4 - Exercises 1–6 give the positions s = f(t) of a...Ch. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - Particle motion At time t, the position of a body...Ch. 3.4 - Particle motion At time t ≥ 0, the velocity of a...Ch. 3.4 - Prob. 9ECh. 3.4 - Lunar projectile motion A rock thrown vertically...Ch. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Free fall from the Tower of Pisa Had Galileo...Ch. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Prob. 24ECh. 3.4 - Prob. 25ECh. 3.4 - Prob. 26ECh. 3.4 - Prob. 27ECh. 3.4 - Draining a tank The number of gallons of water in...Ch. 3.4 - Prob. 29ECh. 3.4 - Inflating a balloon The volume V = (4/3)πr3 of a...Ch. 3.4 - Prob. 31ECh. 3.4 - Prob. 32ECh. 3.4 - Prob. 33ECh. 3.4 - Prob. 34ECh. 3.4 - Prob. 35ECh. 3.4 - Prob. 36ECh. 3.5 - In Exercises 1–18, find dy/dx.
1. y = −10x + 3 cos...Ch. 3.5 - In Exercises 1–18, find dy/dx.
2.
Ch. 3.5 - Prob. 3ECh. 3.5 - In Exercises 1–18, find dy/dx.
4.
Ch. 3.5 - In Exercises 1–18, find dy/dx.
5.
Ch. 3.5 - In Exercises 1–18, find dy/dx.
6.
Ch. 3.5 - In Exercises 1–18, find dy/dx.
7. f(x) = sin x tan...Ch. 3.5 - In Exercises 1–18, find dy/dx.
8.
Ch. 3.5 - In Exercises 1–18, find dy/dx.
9.
Ch. 3.5 - In Exercises 1–18, find dy/dx.
10. y = (sin x +...Ch. 3.5 - Prob. 11ECh. 3.5 - In Exercises 1–18, find dy/dx.
12.
Ch. 3.5 - Prob. 13ECh. 3.5 - Prob. 14ECh. 3.5 - Prob. 15ECh. 3.5 - Prob. 16ECh. 3.5 - In Exercises 1-18, find dy/dx.
Ch. 3.5 - Prob. 18ECh. 3.5 - Prob. 19ECh. 3.5 - Prob. 20ECh. 3.5 - Prob. 21ECh. 3.5 - Prob. 22ECh. 3.5 - In Exercises 23-26, find dr/dθ.
Ch. 3.5 - In Exercises 23-26, find dr/dθ.
Ch. 3.5 - Prob. 25ECh. 3.5 - Prob. 26ECh. 3.5 - Prob. 27ECh. 3.5 - Prob. 28ECh. 3.5 - Prob. 29ECh. 3.5 - Prob. 30ECh. 3.5 - In Exercises 27–32, find dp/dq.
31.
Ch. 3.5 - Prob. 32ECh. 3.5 - Prob. 33ECh. 3.5 - Find y(4) = d4y/dx4 if
y = −2 sin x.
y = 9 cos x.
Ch. 3.5 - Prob. 35ECh. 3.5 - In Exercises 35–38, graph the curves over the...Ch. 3.5 - Prob. 37ECh. 3.5 - Prob. 38ECh. 3.5 - Prob. 39ECh. 3.5 - Prob. 40ECh. 3.5 - Prob. 41ECh. 3.5 - Do the graphs of the functions in Exercises 39–44...Ch. 3.5 - Prob. 43ECh. 3.5 - Prob. 44ECh. 3.5 - Prob. 45ECh. 3.5 - Prob. 46ECh. 3.5 - In Exercises 47 and 48, find an equation for (a)...Ch. 3.5 - Prob. 48ECh. 3.5 - Find the limits in Exercises 49–56.
49.
Ch. 3.5 - Prob. 50ECh. 3.5 - Prob. 51ECh. 3.5 - Find the limits in Exercises 49–56.
52.
Ch. 3.5 - Prob. 53ECh. 3.5 - Prob. 54ECh. 3.5 - Find the limits in Exercises 49–56.
55.
Ch. 3.5 - Find the limits in Exercises 49–56.
56.
Ch. 3.5 - Prob. 57ECh. 3.5 - The equations in Exercises 57 and 58 give the...Ch. 3.5 - Prob. 59ECh. 3.5 - Prob. 60ECh. 3.5 - By computing the first few derivatives and looking...Ch. 3.5 - Derive the formula for the derivative with respect...Ch. 3.5 - A weight is attached to a spring and reaches its...Ch. 3.5 - Assume that a particle’s position on the x-axis is...Ch. 3.5 - Graph y = cos x for −π ≤ x ≤ 2π. On the same...Ch. 3.5 - Graph y = −sin x for −π ≤ x ≤ 2π. On the same...Ch. 3.5 - Centered difference quotients The centered...Ch. 3.5 - Prob. 68ECh. 3.5 - Prob. 69ECh. 3.5 - Prob. 70ECh. 3.5 - Prob. 71ECh. 3.5 - Prob. 72ECh. 3.6 - Derivative Calculations
In Exercises 1–8, given y...Ch. 3.6 - Derivative Calculations
In Exercises 1–8, given y...Ch. 3.6 - Derivative Calculation
In Exercises 1–8, given y =...Ch. 3.6 - Prob. 4ECh. 3.6 - Prob. 5ECh. 3.6 - Derivation Calculations
In Exercises 1–8, given y...Ch. 3.6 - Derivative Calculations
In Exercises 1–8, given y...Ch. 3.6 - Derivative Calculations
In Exercises 1–8, given y...Ch. 3.6 - Prob. 9ECh. 3.6 - In Exercises 9–22, write the function in the form...Ch. 3.6 - In Exercises 9–22, write the function in the form...Ch. 3.6 - Prob. 12ECh. 3.6 - Prob. 13ECh. 3.6 - In Exercises 9–22, write the function in the form...Ch. 3.6 - In Exercises 9–22, write the function in the form...Ch. 3.6 - Prob. 16ECh. 3.6 - In Exercises 9–22, write the function in the form...Ch. 3.6 - Prob. 18ECh. 3.6 - Prob. 19ECh. 3.6 - In Exercises 9–22, write the function in the form...Ch. 3.6 - Prob. 21ECh. 3.6 - Prob. 22ECh. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Prob. 27ECh. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Prob. 30ECh. 3.6 - Prob. 31ECh. 3.6 - Prob. 32ECh. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Prob. 37ECh. 3.6 - Prob. 38ECh. 3.6 - Prob. 39ECh. 3.6 - Prob. 40ECh. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Prob. 43ECh. 3.6 - Prob. 44ECh. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Prob. 49ECh. 3.6 - Prob. 50ECh. 3.6 - Prob. 51ECh. 3.6 - In Exercises 51–70, find dy/dt.
52. y = sec2 πt
Ch. 3.6 - Prob. 53ECh. 3.6 - Prob. 54ECh. 3.6 - Prob. 55ECh. 3.6 - Prob. 56ECh. 3.6 - Prob. 57ECh. 3.6 - Prob. 58ECh. 3.6 - Prob. 59ECh. 3.6 - In Exercises 51–70, find dy/dt.
60.
Ch. 3.6 - In Exercises 51–70, find dy/dt.
61. y = sin (cos...Ch. 3.6 - Prob. 62ECh. 3.6 - Prob. 63ECh. 3.6 - In Exercises 51–70, find dy/dt.
64.
Ch. 3.6 - Prob. 65ECh. 3.6 - In Exercises 51–70, find dy/dt.
66.
Ch. 3.6 - Prob. 67ECh. 3.6 - Prob. 68ECh. 3.6 - Prob. 69ECh. 3.6 - In Exercises 51–70, find dy/dt.
70.
Ch. 3.6 - Second Derivatives
Find y″ in Exercises 71–78.
71....Ch. 3.6 - Prob. 72ECh. 3.6 - Prob. 73ECh. 3.6 - Second Derivatives
Find y″ in Exercises 71–78.
74....Ch. 3.6 - Prob. 75ECh. 3.6 - Prob. 76ECh. 3.6 - Prob. 77ECh. 3.6 - Prob. 78ECh. 3.6 - Prob. 79ECh. 3.6 - Prob. 80ECh. 3.6 - Prob. 81ECh. 3.6 - Finding Derivative values
In Exercises 81–86, find...Ch. 3.6 - Finding Derivative values
In Exercises 81–86, find...Ch. 3.6 - Prob. 84ECh. 3.6 - Finding Derivative values
In Exercises 81–86, find...Ch. 3.6 - Prob. 86ECh. 3.6 - Assume that f′(3) = −1, g′(2) = 5, g(2) = 3, and y...Ch. 3.6 - Prob. 88ECh. 3.6 - Suppose that functions f and g and their...Ch. 3.6 - Suppose that the functions f and g and their...Ch. 3.6 - Find ds/dt when θ = 3π/2 if s = cos θ and dθ/dt =...Ch. 3.6 - Prob. 92ECh. 3.6 - What happens if you can write a function as a...Ch. 3.6 - Prob. 94ECh. 3.6 - Prob. 95ECh. 3.6 - Find the tangent line to at x = 2.
Ch. 3.6 - Prob. 97ECh. 3.6 - Prob. 98ECh. 3.6 - Suppose that a piston is moving straight up and...Ch. 3.6 - Prob. 100ECh. 3.6 - Particle motion The position of a particle moving...Ch. 3.6 - Suppose that the velocity of a falling body is ...Ch. 3.6 - The velocity of a heavy meteorite entering
Earth’s...Ch. 3.6 - Prob. 104ECh. 3.6 - For oscillations of small amplitude (short...Ch. 3.6 - Prob. 106ECh. 3.6 - Prob. 107ECh. 3.6 - Prob. 108ECh. 3.6 - Using the Chain Rule, show that the Power Rule...Ch. 3.6 - Using the Chain Rule, show that the Power Rule...Ch. 3.6 - Consider the function
Show that f is continuous...Ch. 3.6 - Prob. 112ECh. 3.6 - Verify each of the following statements.
If f is...Ch. 3.6 - As the accompanying figure shows, the...Ch. 3.6 - Prob. 115ECh. 3.7 - Differentiating Implicitly
Use implicit...Ch. 3.7 - Differentiating Implicitly
Use implicit...Ch. 3.7 - Differentiating Implicitly
Use implicit...Ch. 3.7 - Differentiating Implicitly
Use implicit...Ch. 3.7 - Use implicit differentiation to find dy/dx in...Ch. 3.7 - Differentiating Implicitly
Use implicit...Ch. 3.7 - Prob. 7ECh. 3.7 - Prob. 8ECh. 3.7 - Prob. 9ECh. 3.7 - Prob. 10ECh. 3.7 - Differentiating implicitly
Use implicit...Ch. 3.7 - Use implicit differentiation to find dy/dx in...Ch. 3.7 - Differentiating Implicitly
Use implicit...Ch. 3.7 - Prob. 14ECh. 3.7 - Prob. 15ECh. 3.7 - Prob. 16ECh. 3.7 - Prob. 17ECh. 3.7 - Prob. 18ECh. 3.7 - Prob. 19ECh. 3.7 - Find dr / d in Exercises 17–20.
cos r + cot =...Ch. 3.7 - In Exercises 21−28, use implicit differentiation...Ch. 3.7 - In Exercises 21−28, use implicit differentiation...Ch. 3.7 - Prob. 23ECh. 3.7 - Prob. 24ECh. 3.7 - In Exercises 21–28, use implicit differentiation...Ch. 3.7 - Prob. 26ECh. 3.7 - Prob. 27ECh. 3.7 - In Exercises 21–28, use implicit differentiation...Ch. 3.7 - If , find the value of at the point (2, 2).
Ch. 3.7 - Prob. 30ECh. 3.7 - In Exercises 31 and 32, find the slope of the...Ch. 3.7 - In Exercises 31 and 32, find the slope of the...Ch. 3.7 - Prob. 33ECh. 3.7 - In Exercises 33−42, verify that the given point is...Ch. 3.7 - In Exercises 33−42, verify that the given point is...Ch. 3.7 - Prob. 36ECh. 3.7 - In Exercises 33−42, verify that the given point is...Ch. 3.7 - In Exercises 33–42, verify that the given point is...Ch. 3.7 - In Exercises 33−42, verify that the given point is...Ch. 3.7 - Exercises 33–42, verify that the given point is on...Ch. 3.7 - In Exercises 33−42, verify that the given point is...Ch. 3.7 - In Exercises 33−42, verify that the given point is...Ch. 3.7 - Parallel tangent lines Find the two points where...Ch. 3.7 - Normal lines parallel to a line Find the normal...Ch. 3.7 - The eight curve Find the slopes of the curve y4 =...Ch. 3.7 - The cissoid of Diocles (from about 200 b.c.) Find...Ch. 3.7 - The devil’s curve (Gabriel Gramer, 1750) Find the...Ch. 3.7 - The folium of Descartes (See Figure 3.29)
Find the...Ch. 3.7 - Prob. 49ECh. 3.7 - Power rule for rational exponents Let p and q be...Ch. 3.7 - Prob. 51ECh. 3.7 - Prob. 52ECh. 3.7 - Prob. 53ECh. 3.7 - The graph of is called a semicubical parabola and...Ch. 3.7 - In Exercises 55 and 56, find both (treating y as...Ch. 3.7 - Prob. 56ECh. 3.7 - Derivative of arcsine Assume that y = sin−1x is a...Ch. 3.7 - Prob. 58ECh. 3.8 - In Exercises 1–4:
Find f–1(x).
Graph f and f–1...Ch. 3.8 - In Exercises 1–4:
Find f–1(x).
Graph f and f–1...Ch. 3.8 - In Exercises 1–4:
Find f–1(x).
Graph f and f–1...Ch. 3.8 - Prob. 4ECh. 3.8 - Show that f(x) = x3 and are inverses of one...Ch. 3.8 - Prob. 6ECh. 3.8 - Let f(x) = x3 – 3x2 – 1, x ≥ 2. Find the value of...Ch. 3.8 - Prob. 8ECh. 3.8 - Suppose that the differentiable function y = f(x)...Ch. 3.8 - Prob. 10ECh. 3.8 - Derivatives of Logarithms
In Exercises 11–40, find...Ch. 3.8 - Derivatives of Logarithms
In Exercises 11–40, find...Ch. 3.8 - Derivatives of Logarithms
In Exercises 11–40, find...Ch. 3.8 - Derivatives of Logarithms
In Exercises 11–40, find...Ch. 3.8 - Derivatives of Logarithms
In Exercises 11–40, find...Ch. 3.8 - Derivatives of Logarithms
In Exercises 11–40, find...Ch. 3.8 - Prob. 17ECh. 3.8 - Derivatives of Logarithms
In Exercises 11-40, find...Ch. 3.8 - Derivatives of Logarithms
In Exercises 11-40, find...Ch. 3.8 - Prob. 20ECh. 3.8 - Derivatives of Logarithms
In Exercises 11-40, find...Ch. 3.8 - Derivatives of Logarithms
In Exercises 11-40, find...Ch. 3.8 - Prob. 23ECh. 3.8 - In Exercises 11-40, find the derivative of y with...Ch. 3.8 - In Exercises 11-40, find the derivative of y with...Ch. 3.8 - Prob. 26ECh. 3.8 - In Exercises 11-40, find the derivative of y with...Ch. 3.8 - In Exercises 11-40, find the derivative of y with...Ch. 3.8 - In Exercises 11-40, find the derivative of y with...Ch. 3.8 - Prob. 30ECh. 3.8 - Prob. 31ECh. 3.8 - Prob. 32ECh. 3.8 - In Exercises 11-40, find the derivative of y with...Ch. 3.8 - In Exercises 11-40, find the derivative of y with...Ch. 3.8 - In Exercises 11-40, find the derivative of y with...Ch. 3.8 - In Exercises 11-40, find the derivative of y with...Ch. 3.8 - Prob. 37ECh. 3.8 - In Exercises 11-40, find the derivative of y with...Ch. 3.8 - Prob. 39ECh. 3.8 - Prob. 40ECh. 3.8 - In Exercises 41-54, use logarithmic...Ch. 3.8 - Prob. 42ECh. 3.8 - In Exercises 41-54, use logarithmic...Ch. 3.8 - Prob. 44ECh. 3.8 - Prob. 45ECh. 3.8 - Prob. 46ECh. 3.8 - In Exercises 41-54, use logarithmic...Ch. 3.8 - In Exercises 41-54, use logarithmic...Ch. 3.8 - Prob. 49ECh. 3.8 - Prob. 50ECh. 3.8 - In Exercises 41-54, use logarithmic...Ch. 3.8 - Prob. 52ECh. 3.8 - In Exercises 41-54, use logarithmic...Ch. 3.8 - Prob. 54ECh. 3.8 - Prob. 55ECh. 3.8 - Prob. 56ECh. 3.8 - In Exercises 55-62, find the derivative of y with...Ch. 3.8 - Prob. 58ECh. 3.8 - In Exercises 55-62, find the derivative of y with...Ch. 3.8 - Prob. 60ECh. 3.8 - Prob. 61ECh. 3.8 - Prob. 62ECh. 3.8 - Prob. 63ECh. 3.8 - Prob. 64ECh. 3.8 - Prob. 65ECh. 3.8 - Prob. 66ECh. 3.8 - In Exercises 67-88, find the derivative of y with...Ch. 3.8 - Prob. 68ECh. 3.8 - In Exercises 67-88, find the derivative of y with...Ch. 3.8 - In Exercises 67–88, find the derivative of y with...Ch. 3.8 - In Exercises 67-88, find the derivative of y with...Ch. 3.8 - Prob. 72ECh. 3.8 - In Exercises 67-88, find the derivative of y with...Ch. 3.8 - Prob. 74ECh. 3.8 - Prob. 75ECh. 3.8 - Prob. 76ECh. 3.8 - In Exercises 67-88, find the derivative of y with...Ch. 3.8 - Prob. 78ECh. 3.8 - Prob. 79ECh. 3.8 - In Exercises 67-88, find the derivative of y with...Ch. 3.8 - Prob. 81ECh. 3.8 - In Exercises 67-88, find the derivative of y with...Ch. 3.8 - In Exercises 67-88, find the derivative of y with...Ch. 3.8 - In Exercises 67-88, find the derivative of y with...Ch. 3.8 - In Exercises 67-88, find the derivative of y with...Ch. 3.8 - Prob. 86ECh. 3.8 - Prob. 87ECh. 3.8 - Prob. 88ECh. 3.8 - In Exercises 89-100, use logarithmic...Ch. 3.8 - Prob. 90ECh. 3.8 - Prob. 91ECh. 3.8 - Prob. 92ECh. 3.8 - Prob. 93ECh. 3.8 - In Exercises 89−100, use logarithmic...Ch. 3.8 - In Exercises 89−100, use logarithmic...Ch. 3.8 - Prob. 96ECh. 3.8 - Prob. 97ECh. 3.8 - In Exercises 89−100, use logarithmic...Ch. 3.8 - In Exercises 89−100, use logarithmic...Ch. 3.8 - In Exercises 89−100, use logarithmic...Ch. 3.8 - Prob. 101ECh. 3.8 - Show that for any x > 0.
Ch. 3.8 - If f(x) = xn, n ≥ 1, show from the definition of...Ch. 3.8 - Using mathematical induction, show that for n >...Ch. 3.9 - Use reference triangles in an appropriate...Ch. 3.9 - Prob. 2ECh. 3.9 - Use reference triangles in an appropriate...Ch. 3.9 - Use reference triangles in an appropriate...Ch. 3.9 - Use reference triangles in an appropriate...Ch. 3.9 - Prob. 6ECh. 3.9 - Use reference triangles in an appropriate...Ch. 3.9 - Prob. 8ECh. 3.9 - Find the values in Exercises 9–12.
9.
Ch. 3.9 - Find the values in Exercises 9–12.
10.
Ch. 3.9 - Find the values in Exercises 9–12.
11.
Ch. 3.9 - Find the values in Exercises 9–12.
12.
Ch. 3.9 - Find the limits in Exercises 13–20. (If in doubt,...Ch. 3.9 - Prob. 14ECh. 3.9 - Find the limits in Exercises 13–20. (If in doubt,...Ch. 3.9 - Find the limits in Exercises 13–20. (If in doubt,...Ch. 3.9 - Find the limits in Exercises 13–20. (If in doubt,...Ch. 3.9 - Prob. 18ECh. 3.9 - Find the limits in Exercises 13–20. (If in doubt,...Ch. 3.9 - Prob. 20ECh. 3.9 - In Exercises 21–42, find the derivative of y with...Ch. 3.9 - In Exercises 21–42, find the derivative of y with...Ch. 3.9 - In Exercises 21–42, find the derivative of y with...Ch. 3.9 - Prob. 24ECh. 3.9 - Prob. 25ECh. 3.9 - Prob. 26ECh. 3.9 - Prob. 27ECh. 3.9 - Prob. 28ECh. 3.9 - In Exercises 21–42, find the derivative of y with...Ch. 3.9 - In Exercises 21–42, find the derivative of y with...Ch. 3.9 - In Exercises 21–42, find the derivative of y with...Ch. 3.9 - Prob. 32ECh. 3.9 - In Exercises 21–42, find the derivative of y with...Ch. 3.9 - In Exercises 21–42, find the derivative of y with...Ch. 3.9 - In Exercises 21–42, find the derivative of y with...Ch. 3.9 - Prob. 36ECh. 3.9 - In Exercises 21–42, find the derivative of y with...Ch. 3.9 - Prob. 38ECh. 3.9 - Prob. 39ECh. 3.9 - Prob. 40ECh. 3.9 - In Exercises 21–42, find the derivative of y with...Ch. 3.9 - Prob. 42ECh. 3.9 - For problems 43-46 use implicit differentiation to...Ch. 3.9 - Prob. 44ECh. 3.9 - For problems 43-46 use implicit differentiation to...Ch. 3.9 - Prob. 46ECh. 3.9 - You are sitting in a classroom next to the wall...Ch. 3.9 - Find the angle α
Ch. 3.9 - Here is an informal proof that Explain what is...Ch. 3.9 - Prob. 50ECh. 3.9 - Which of the expressions in Exercises 51–54 are...Ch. 3.9 - Prob. 52ECh. 3.9 - Which of the expressions in Exercises 51–54 are...Ch. 3.9 - Prob. 54ECh. 3.9 - Prob. 55ECh. 3.9 - Derive the formula
for the derivative of y =...Ch. 3.9 - Prob. 57ECh. 3.9 - Prob. 58ECh. 3.9 - Prob. 59ECh. 3.9 - Prob. 60ECh. 3.9 - Prob. 61ECh. 3.9 - Prob. 62ECh. 3.9 - Prob. 63ECh. 3.9 - Prob. 64ECh. 3.9 - Prob. 65ECh. 3.9 - Prob. 66ECh. 3.9 - Prob. 67ECh. 3.9 - Prob. 68ECh. 3.9 - Prob. 69ECh. 3.9 - Prob. 70ECh. 3.10 - Area Suppose that the radius r and area A = πr2 of...Ch. 3.10 - Surface area Suppose that the radius r and surface...Ch. 3.10 - Prob. 3ECh. 3.10 - Prob. 4ECh. 3.10 - Prob. 5ECh. 3.10 - Prob. 6ECh. 3.10 - Prob. 7ECh. 3.10 - Prob. 8ECh. 3.10 - Prob. 9ECh. 3.10 - If r + s2 + v3 = 12, dr/dt = 4, and ds/dt = −3,...Ch. 3.10 - If the original 24 m edge length x of a cube...Ch. 3.10 - Prob. 12ECh. 3.10 - Volume The radius r and height h of a right...Ch. 3.10 - Volume The radius r and height h of a right...Ch. 3.10 - Changing voltage The voltage V (volts), current I...Ch. 3.10 - Prob. 16ECh. 3.10 - Prob. 17ECh. 3.10 - Prob. 18ECh. 3.10 - Prob. 19ECh. 3.10 - Prob. 20ECh. 3.10 - Changing dimensions in a rectangle The length l of...Ch. 3.10 - Changing dimensions in a rectangular box Suppose...Ch. 3.10 - A sliding ladder A 13-ft ladder is leaning against...Ch. 3.10 - Prob. 24ECh. 3.10 - Flying a kite A girl flies a kite at a height of...Ch. 3.10 - Prob. 26ECh. 3.10 - Prob. 27ECh. 3.10 - Prob. 28ECh. 3.10 - Prob. 29ECh. 3.10 - Prob. 30ECh. 3.10 - The radius of an inflating balloon A spherical...Ch. 3.10 - Prob. 32ECh. 3.10 - Prob. 33ECh. 3.10 - Prob. 34ECh. 3.10 - Cardiac output In the late 1860s, Adolf Fick, a...Ch. 3.10 - Prob. 36ECh. 3.10 - Motion in the plane The coordinates of a particle...Ch. 3.10 - Prob. 38ECh. 3.10 - Prob. 39ECh. 3.10 - Prob. 40ECh. 3.10 - Prob. 41ECh. 3.10 - Prob. 42ECh. 3.10 - Baseball players A baseball diamond is a square 90...Ch. 3.10 - Prob. 44ECh. 3.10 - Prob. 45ECh. 3.10 - Prob. 46ECh. 3.10 - A lighthouse beam A lighthouse sits 1 km offshore,...Ch. 3.11 - find the linearization L(x) of f(x) at x = a.
Ch. 3.11 - find the linearization L(x) of f(x) at x = a.
Ch. 3.11 - find the linearization L(x) of f(x) at x = a.
Ch. 3.11 - find the linearization L(x) of f(x) at x = a.
Ch. 3.11 - find the linearization L(x) of f(x) at x = a.
Ch. 3.11 - Prob. 6ECh. 3.11 - Prob. 7ECh. 3.11 - Prob. 8ECh. 3.11 - Prob. 9ECh. 3.11 - Prob. 10ECh. 3.11 - find a linearization at a suitably chosen integer...Ch. 3.11 - Prob. 12ECh. 3.11 - Prob. 13ECh. 3.11 - Prob. 14ECh. 3.11 - Show that the linearization of f(x) = (1 + x)k at...Ch. 3.11 - Prob. 16ECh. 3.11 - Use the approximation (1 + x)k ≈
1 + kx to...Ch. 3.11 - Prob. 18ECh. 3.11 - find dy.
Ch. 3.11 - Prob. 20ECh. 3.11 - find dy.
Ch. 3.11 - Prob. 22ECh. 3.11 - Prob. 23ECh. 3.11 - Prob. 24ECh. 3.11 - find dy.
Ch. 3.11 - Prob. 26ECh. 3.11 - Prob. 27ECh. 3.11 - Prob. 28ECh. 3.11 - Prob. 29ECh. 3.11 - Prob. 30ECh. 3.11 - In Exercises 19-38, find dy.
31.
Ch. 3.11 - Prob. 32ECh. 3.11 - Prob. 33ECh. 3.11 - Prob. 34ECh. 3.11 - Prob. 35ECh. 3.11 - Prob. 36ECh. 3.11 - In Exercises 19-38, find dy.
37. y = sec−1(e−x)
Ch. 3.11 - Prob. 38ECh. 3.11 - In Exercises 39-14, each function f(x) changes...Ch. 3.11 - Prob. 40ECh. 3.11 - Prob. 41ECh. 3.11 - Prob. 42ECh. 3.11 - Prob. 43ECh. 3.11 - Prob. 44ECh. 3.11 - In Exercises 45-50, write a differential formula...Ch. 3.11 - Prob. 46ECh. 3.11 - In Exercises 45-50, write a differential formula...Ch. 3.11 - Prob. 48ECh. 3.11 - In Exercises 45-50, write a differential formula...Ch. 3.11 - Prob. 50ECh. 3.11 - The radius of a circle is increased from 2.00 to...Ch. 3.11 - Prob. 52ECh. 3.11 - Estimate the volume of material in a cylindrical...Ch. 3.11 - Prob. 54ECh. 3.11 - The radius r of a circle is measured with an error...Ch. 3.11 - Prob. 56ECh. 3.11 - The height and radius of a right circular cylinder...Ch. 3.11 - Prob. 58ECh. 3.11 - The diameter of a sphere is measured as 100 ± 1 cm...Ch. 3.11 - Prob. 60ECh. 3.11 - Prob. 61ECh. 3.11 - Prob. 62ECh. 3.11 - Prob. 63ECh. 3.11 - Prob. 64ECh. 3.11 - Quadratic approximations
Let Q(x) = b0 + b1 (x −...Ch. 3.11 - Prob. 66ECh. 3.11 - Prob. 67ECh. 3.11 - Prob. 68ECh. 3 - Prob. 1GYRCh. 3 - Prob. 2GYRCh. 3 - Prob. 3GYRCh. 3 - Prob. 4GYRCh. 3 - Prob. 5GYRCh. 3 - Prob. 6GYRCh. 3 - Prob. 7GYRCh. 3 - Prob. 8GYRCh. 3 - Prob. 9GYRCh. 3 - What formula do we need, in addition to the three...Ch. 3 - Prob. 11GYRCh. 3 - What is the derivative of the exponential function...Ch. 3 - Prob. 13GYRCh. 3 - Prob. 14GYRCh. 3 - Prob. 15GYRCh. 3 - Prob. 16GYRCh. 3 - Prob. 17GYRCh. 3 - Prob. 18GYRCh. 3 - Prob. 19GYRCh. 3 - Prob. 20GYRCh. 3 - Prob. 21GYRCh. 3 - Prob. 22GYRCh. 3 - Prob. 23GYRCh. 3 - Prob. 24GYRCh. 3 - Prob. 25GYRCh. 3 - Prob. 26GYRCh. 3 - Prob. 27GYRCh. 3 - Prob. 28GYRCh. 3 - Prob. 29GYRCh. 3 - Prob. 30GYRCh. 3 - Prob. 31GYRCh. 3 - Prob. 32GYRCh. 3 - Prob. 33GYRCh. 3 - Find the derivatives of the functions in Exercises...Ch. 3 - Prob. 2PECh. 3 - Prob. 3PECh. 3 - Prob. 4PECh. 3 - Find the derivatives of the functions in Exercises...Ch. 3 - Prob. 6PECh. 3 - Prob. 7PECh. 3 - Prob. 8PECh. 3 - Prob. 9PECh. 3 - Prob. 10PECh. 3 - Prob. 11PECh. 3 - Prob. 12PECh. 3 - Prob. 13PECh. 3 - Prob. 14PECh. 3 - Prob. 15PECh. 3 - Prob. 16PECh. 3 - Prob. 17PECh. 3 - Prob. 18PECh. 3 - Prob. 19PECh. 3 - Prob. 20PECh. 3 - Prob. 21PECh. 3 - Prob. 22PECh. 3 - Prob. 23PECh. 3 - Prob. 24PECh. 3 - Prob. 25PECh. 3 - Prob. 26PECh. 3 - Prob. 27PECh. 3 - Prob. 28PECh. 3 - Find the derivatives of the functions in Exercises...Ch. 3 - Prob. 30PECh. 3 - Prob. 31PECh. 3 - Prob. 32PECh. 3 - Prob. 33PECh. 3 - Prob. 34PECh. 3 - Prob. 35PECh. 3 - Prob. 36PECh. 3 - Prob. 37PECh. 3 - Prob. 38PECh. 3 - Prob. 39PECh. 3 - Prob. 40PECh. 3 - Prob. 41PECh. 3 - Prob. 42PECh. 3 - Prob. 43PECh. 3 - Prob. 44PECh. 3 - Find the derivatives of the functions in Exercises...Ch. 3 - Prob. 46PECh. 3 - Find the derivatives of the functions in Exercises...Ch. 3 - Prob. 48PECh. 3 - Find the derivatives of the functions in Exercises...Ch. 3 - Prob. 50PECh. 3 - Prob. 51PECh. 3 - Prob. 52PECh. 3 - Find the derivatives of the functions in Exercises...Ch. 3 - Prob. 54PECh. 3 - Prob. 55PECh. 3 - Prob. 56PECh. 3 - Find the derivatives of the functions in Exercises...Ch. 3 - Prob. 58PECh. 3 - Find the derivatives of the functions in Exercises...Ch. 3 - Prob. 60PECh. 3 - Prob. 61PECh. 3 - Prob. 62PECh. 3 - Prob. 63PECh. 3 - Prob. 64PECh. 3 - In Exercises 65-78, find dy/dx by implicit...Ch. 3 - Prob. 66PECh. 3 - In Exercises 65-78, find dy/dx by implicit...Ch. 3 - Prob. 68PECh. 3 - Prob. 69PECh. 3 - Prob. 70PECh. 3 - Prob. 71PECh. 3 - Prob. 72PECh. 3 - Prob. 73PECh. 3 - Prob. 74PECh. 3 - In Exercises 65-78, find dy/dx by implicit...Ch. 3 - Prob. 76PECh. 3 - Prob. 77PECh. 3 - Prob. 78PECh. 3 - Prob. 79PECh. 3 - Prob. 80PECh. 3 - Prob. 81PECh. 3 - Prob. 82PECh. 3 - Find d2y/dx2 by implicit differentiation:
x3 + y3...Ch. 3 - Prob. 84PECh. 3 - Prob. 85PECh. 3 - Prob. 86PECh. 3 - Prob. 87PECh. 3 - Prob. 88PECh. 3 - Prob. 89PECh. 3 - Prob. 90PECh. 3 - Prob. 91PECh. 3 - Prob. 92PECh. 3 - In Exercises 93 and 94, find the derivative using...Ch. 3 - Prob. 94PECh. 3 - Prob. 95PECh. 3 - Prob. 96PECh. 3 - Prob. 97PECh. 3 - Prob. 98PECh. 3 - Tangent lines with specified slope Are there any...Ch. 3 - Prob. 100PECh. 3 - Prob. 101PECh. 3 - Prob. 102PECh. 3 - Tangent lines perpendicular or parallel to lines...Ch. 3 - Prob. 104PECh. 3 - Prob. 105PECh. 3 - Prob. 106PECh. 3 - Tangent parabola The parabola y = x2 + C is to be...Ch. 3 - Prob. 108PECh. 3 - Prob. 109PECh. 3 - Prob. 110PECh. 3 - Prob. 111PECh. 3 - Prob. 112PECh. 3 - Prob. 113PECh. 3 - Prob. 114PECh. 3 - Prob. 115PECh. 3 - Prob. 116PECh. 3 - Prob. 117PECh. 3 - Prob. 118PECh. 3 - Each of the figures in Exercises 119 and 120 shows...Ch. 3 - Prob. 120PECh. 3 - Prob. 121PECh. 3 - Prob. 122PECh. 3 - Prob. 123PECh. 3 - Prob. 124PECh. 3 - Find the limits in Exercises 125–132.
125.
Ch. 3 - Prob. 126PECh. 3 - Find the limits in Exercises 125–132.
127.
Ch. 3 - Prob. 128PECh. 3 - Prob. 129PECh. 3 - Prob. 130PECh. 3 - Find the limits in Exercises 125–132.
131.
Ch. 3 - Prob. 132PECh. 3 - Prob. 133PECh. 3 - Prob. 134PECh. 3 - In Exercises 135–140, use logarithmic...Ch. 3 - Prob. 136PECh. 3 - In Exercises 135–140, use logarithmic...Ch. 3 - Prob. 138PECh. 3 - In Exercises 135–140, use logarithmic...Ch. 3 - Prob. 140PECh. 3 - Prob. 141PECh. 3 - Prob. 142PECh. 3 - Circle’s changing area The radius r of a circle is...Ch. 3 - Cube’s changing edges The volume of a cube is...Ch. 3 - Prob. 145PECh. 3 - Prob. 146PECh. 3 - Speed of moving particle The coordinates of a...Ch. 3 - Motion of a particle A particle moves along the...Ch. 3 - Draining a tank Water drains from the conical tank...Ch. 3 - Rotating spool As television cable is pulled from...Ch. 3 - Moving searchlight beam The figure shows a boat 1...Ch. 3 - Prob. 152PECh. 3 - Find the linearizations of
tan x at x = −π/4
sec x...Ch. 3 - Prob. 154PECh. 3 - Find the linearization of at x = 0.
Ch. 3 - Prob. 156PECh. 3 - Surface area of a cone Write a formula that...Ch. 3 - Prob. 158PECh. 3 - Compounding error The circumference of the equator...Ch. 3 - Finding height To find the height of a lamppost...Ch. 3 - Prob. 1AAECh. 3 - Prob. 2AAECh. 3 - Prob. 3AAECh. 3 - Solutions to differential equations
Show that y =...Ch. 3 - Prob. 5AAECh. 3 - Prob. 6AAECh. 3 - Prob. 7AAECh. 3 - Prob. 8AAECh. 3 - Prob. 9AAECh. 3 - Motion of a particle The position at time t ≥ 0 of...Ch. 3 - Shooting a paper clip On Earth, you can easily...Ch. 3 - Velocities of two particles At time t sec, the...Ch. 3 - Prob. 13AAECh. 3 - Prob. 14AAECh. 3 - Prob. 15AAECh. 3 - Prob. 16AAECh. 3 - Find all values of the constants m and b for which...Ch. 3 - Prob. 18AAECh. 3 - Prob. 19AAECh. 3 - Prob. 20AAECh. 3 - Prob. 21AAECh. 3 - Even differentiable functions Is there anything...Ch. 3 - Suppose that the functions f and g are defined...Ch. 3 - (Continuation of Exercise 23.) Use the result of...Ch. 3 - Is the derivative of
continuous at x = 0? How...Ch. 3 - Prob. 26AAECh. 3 - Prob. 27AAECh. 3 - Prob. 28AAECh. 3 - Prob. 29AAECh. 3 - Leibniz’s rule for higher-order derivatives of...Ch. 3 - Prob. 31AAECh. 3 - Prob. 32AAE
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