Thomas' Calculus - With MyMathLab
14th Edition
ISBN: 9780134665672
Author: Hass
Publisher: PEARSON
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Chapter A.3, Problem 36E
To determine
Write a pair of inequalities that describes the points that lie inside the circle with the center
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If a snowball melts so that its surface area decreases at a rate of 10 cm²/min, find the rate (in cm/min) at which the diameter decreases when the diameter is 12 cm. (Round your answer to three decimal places.)
cm/min
1) let X: N R be a sequence and let Y: N+R
be the squence obtained from x by di scarding
the first meN terms of x in other words
Y(n) = x(m+h) then X converges to L
If and only is y converges to L-
11) let Xn = cos(n) where nyo prove
D2-1
that lim xn
= 0
by def.
h→00
ii) prove that for any irrational numbers ther
exsist asquence of rational numbers (xn)
converg to S.
4.2 Product and Quotient Rules
1.
9(x)=125+1
y14+2
Use the product and/or quotient rule to find the derivative of each function.
a. g(x)=
b. y (2x-3)(x-1)
c. y==
3x-4
√x
Chapter A.3 Solutions
Thomas' Calculus - With MyMathLab
Ch. A.3 - In Exercises 1 and 2, a particle moves from A to B...Ch. A.3 - Prob. 2ECh. A.3 - Describe the graphs of the equations in
Ch. A.3 - Prob. 4ECh. A.3 - Prob. 5ECh. A.3 - Prob. 6ECh. A.3 - Prob. 7ECh. A.3 - Prob. 8ECh. A.3 - Prob. 9ECh. A.3 - Prob. 10E
Ch. A.3 - Prob. 11ECh. A.3 - In Exercises 9–15, write an equation for each line...Ch. A.3 - Prob. 13ECh. A.3 - Prob. 14ECh. A.3 - Prob. 15ECh. A.3 - In Exercises 16 and 17, find the line’s x-and...Ch. A.3 - In Exercises 16 and 17, find the line’s x-and...Ch. A.3 - Is there anything special about the relationship...Ch. A.3 - Prob. 19ECh. A.3 - Prob. 20ECh. A.3 - Prob. 21ECh. A.3 - Prob. 22ECh. A.3 - Prob. 23ECh. A.3 - Prob. 24ECh. A.3 - Prob. 25ECh. A.3 - Prob. 26ECh. A.3 - Prob. 27ECh. A.3 - Prob. 28ECh. A.3 - Prob. 29ECh. A.3 - Prob. 30ECh. A.3 - Describe the regions defined by the inequalities...Ch. A.3 - Describe the regions defined by the inequalities...Ch. A.3 - Prob. 33ECh. A.3 - Describe the regions defined by the inequalities...Ch. A.3 - Prob. 35ECh. A.3 - Write a pair of inequalities that describe the...Ch. A.3 - Prob. 37ECh. A.3 - Prob. 38ECh. A.3 - Prob. 39ECh. A.3 - Prob. 40ECh. A.3 - Prob. 41ECh. A.3 - Insulation According to the figure in Exercise 41,...Ch. A.3 - 43. Pressure under water The pressure p...Ch. A.3 - Reflected light A ray of light comes in along the...Ch. A.3 - Prob. 45ECh. A.3 - Prob. 46ECh. A.3 - Prob. 47ECh. A.3 - Show that the triangle with vertices A(0, 0), ,...Ch. A.3 - Prob. 49ECh. A.3 - Prob. 50ECh. A.3 - Prob. 51ECh. A.3 - Prob. 52E
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- 4.2 Product and Quotient Rules 1. Use the product and/or quotient rule to find the derivative of each function. 2.5 a. g(x)=+1 y14+2 √x-1) b. y=(2x-3)(x-:arrow_forward3. The total profit (in dollars) from selling x watches is P(x)=0.52x²-0.0002x². Find and interpret the following. a) P(100) b) P'(100)arrow_forward3. Find the slope and the equation of the tangent line to the graph of the given function at the given value of x. -4 f(x)=x-x³;x=2arrow_forward
- 2. Find the equation of the tangent line to the graph of the given function at the given point. f(x)=(x+3)(2x²-6) at (1,-16)arrow_forward6. Researchers who have been studying the alarming rate at which the level of the Dead Sea has been dropping have shown that the density d (x) (in g per cm³) of the Dead Sea brine during evaporation can be estimated by the function d(x)=1.66 0.90x+0.47x², where x is the fraction of the remaining brine, 0≤x≤1. a) Estimate the density of the brine when 60% of the brine remains. b) Find and interpret the instantaneous rate of change of the density when 60% of the brine remains.arrow_forward5. If g'(5) 10 and h'(5)=-4, find f'(5) for f(x)=4g(x)-2h(x)+3.arrow_forward
- 2. Find each derivative. Write answers with positive exponents. a) Dx 9x -3 [97] b) f'(3) if f(x) = x²-5x² 8arrow_forwardA ladder 27 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed up 6 feet of the ladder, the ladder makes an angle of л/3 with the ground. Answer the two related rates questions below. (Hint: Use two carefully labeled similar right triangles.) (a) If h is the height of the firefighter above the ground, at the instant the angle of the ladder with the ground is л/3, find dh/dt= feet/sec. (b) If w is the horizontal distance from the firefighter to the wall, at the instant the angle of the ladder with the ground is л/3, find dw/dt= feet/sec.arrow_forwardTwo cars start moving from the same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later? Step 1 Using the diagram of a right triangle given below, the relation between x, y, and z is z² = x²+ +12 x Step 2 We must find dz/dt. Differentiating both sides and simplifying gives us the following. 2z dz dt dx 2x. +2y dt dx dy dz x +y dt dt dt 2z dy dt × dx (x+y dt dy dtarrow_forward
- An elastic rope is attached to the ground at the positions shown in the picture. The rope is being pulled up along the dotted line. Assume the units are meters. 9 ground level Assume that x is increasing at a rate of 3 meters/sec. (a) Write as a function of x: 0= (b) When x=10, the angle is changing at a rate of rad/sec. (c) Let L be the the left hand piece of rope and R the right hand piece of rope. When x=10, is the rate of change of L larger than the rate of change of R? ○ Yes ○ Noarrow_forward4.1 Basic Rules of Differentiation. 1. Find the derivative of each function. Write answers with positive exponents. Label your derivatives with appropriate derivative notation. a) y=8x-5x3 4 X b) y=-50 √x+11x -5 c) p(x)=-10x²+6x3³arrow_forwardPlease refer belowarrow_forward
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2.1 Introduction to inequalities; Author: Oli Notes;https://www.youtube.com/watch?v=D6erN5YTlXE;License: Standard YouTube License, CC-BY
GCSE Maths - What are Inequalities? (Inequalities Part 1) #56; Author: Cognito;https://www.youtube.com/watch?v=e_tY6X5PwWw;License: Standard YouTube License, CC-BY
Introduction to Inequalities | Inequality Symbols | Testing Solutions for Inequalities; Author: Scam Squad Math;https://www.youtube.com/watch?v=paZSN7sV1R8;License: Standard YouTube License, CC-BY