Calculus: Early Transcendentals (3rd Edition)
3rd Edition
ISBN: 9780134763644
Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher: PEARSON
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Textbook Question
Chapter 5.1, Problem 6E
The velocity in ft/s of an object moving along a line is given by v – f(t) on the interval 0 < t < 10 (see figure), where t is measured in seconds.
a. Divide the interval [0, 10] into n – 5 subintervals. On each subinterval, assume the object moves at a constant velocity equal to the value of v evaluated at the left endpoint of the subinterval, and use these approximations to estimate the displacement of the object on [0, 10].
b. Repeat part (a) using the right endpoints to estimate the displacement on [0, 10].
c. Repeat part (a) using the midpoints of each subinterval to estimate the displacement on [0, 10].
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Question 3 (6 points)
u, v and w are three coplanar vectors:
⚫ w has a magnitude of 10 and points along the positive x-axis
⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x-
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⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x-
axis
⚫ vector v is located in between u and w
a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane.
b) If possible, find
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Support your answer mathematically or a with a written explanation.
c) If possible, find
v. (ū⋅ w)
Support your answer mathematically or a with a written explanation.
d) If possible, find
u (v × w)
Support your answer mathematically or a with a written explanation.
Note: in this question you can work with the vectors in geometric form or convert
them to algebraic vectors.
K
Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the
limit doesn't exist.
x-7
p(x) =
X-7
Select the correct choice below and, if necessary, fill in the answer box(es) within your choice.
(Use a comma to separate answers as needed.)
OA. f is discontinuous at the single value x =
OB. f is discontinuous at the single value x=
OC. f is discontinuous at the two values x =
OD. f is discontinuous at the two values x =
The limit is
The limit does not exist and is not co or - ∞.
The limit for the smaller value is
The limit for the larger value is
The limit for the smaller value is
The limit for the larger value does not exist and is not c∞ or -
K
x3 +216
complete the table and use the results to find lim k(x).
If k(x) =
X+6
X-6
X
-6.1
-6.01
- 6.001
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-5.9
k(x)
Complete the table.
X
-6.1
-6.01
- 6.001
- 5.999
- 5.99
- 5.9
k(x)
(Round to three decimal places as needed.)
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Chapter 5 Solutions
Calculus: Early Transcendentals (3rd Edition)
Ch. 5.1 - What is the displacement of an object that travels...Ch. 5.1 - In Example 1, if we used n = 32 subintervals of...Ch. 5.1 - If the interval [1, 9] is partitioned into 4...Ch. 5.1 - If the function in Example 2 is replaced with f(x)...Ch. 5.1 - Suppose an object moves along a line at 15 m/s,...Ch. 5.1 - Given the graph of the positive velocity of an...Ch. 5.1 - Prob. 3ECh. 5.1 - The velocity in ft/s or an object moving along a...Ch. 5.1 - The velocity in ft/s of an object moving along a...Ch. 5.1 - The velocity in ft/s of an object moving along a...
Ch. 5.1 - Prob. 7ECh. 5.1 - Explain how Riemann sum approximations to the area...Ch. 5.1 - Prob. 9ECh. 5.1 - Prob. 10ECh. 5.1 - Suppose the interval [1, 3] is partitioned into n...Ch. 5.1 - Prob. 12ECh. 5.1 - Does a right Riemann sum underestimate or...Ch. 5.1 - Does a left Riemann sum underestimate or...Ch. 5.1 - Approximating displacement The velocity in ft/s of...Ch. 5.1 - Approximating displacement The velocity in ft/s of...Ch. 5.1 - Approximating displacement The velocity of an...Ch. 5.1 - Approximating displacement The velocity of an...Ch. 5.1 - Approximating displacement The velocity of an...Ch. 5.1 - Approximating displacement The velocity of an...Ch. 5.1 - Approximating displacement The velocity of an...Ch. 5.1 - Approximating displacement The velocity of an...Ch. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - A midpoint Riemann sum Approximate the area of the...Ch. 5.1 - Prob. 34ECh. 5.1 - Free fall On October 14, 2012, Felix Baumgartner...Ch. 5.1 - Free fall Use geometry and the figure given in...Ch. 5.1 - Prob. 37ECh. 5.1 - Midpoint Riemann sums Complete the following steps...Ch. 5.1 - Prob. 39ECh. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Riemann sums from tables Evaluate the left and...Ch. 5.1 - Prob. 44ECh. 5.1 - Displacement from a table of velocities The...Ch. 5.1 - Displacement from a table of velocities The...Ch. 5.1 - Sigma notation Express the following sums using...Ch. 5.1 - Sigma notation Express the following sums using...Ch. 5.1 - Sigma notation Evaluate the following expressions....Ch. 5.1 - Evaluating sums Evaluate the following expressions...Ch. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Prob. 54ECh. 5.1 - Prob. 55ECh. 5.1 - Prob. 56ECh. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Explain why or why not Determine whether the...Ch. 5.1 - Prob. 60ECh. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.1 - Prob. 63ECh. 5.1 - Prob. 64ECh. 5.1 - Identifying Riemann sums Fill in the blanks with...Ch. 5.1 - Identifying Riemann sums Fill in the blanks with...Ch. 5.1 - Prob. 67ECh. 5.1 - Prob. 68ECh. 5.1 - Approximating areas Estimate the area of the...Ch. 5.1 - Displacement from a velocity graph Consider the...Ch. 5.1 - Displacement from a velocity graph Consider the...Ch. 5.1 - Flow rates Suppose a gauge at the outflow of a...Ch. 5.1 - Mass from density A thin 10-cm rod is made of an...Ch. 5.1 - Prob. 74ECh. 5.1 - Prob. 75ECh. 5.1 - Prob. 76ECh. 5.1 - Prob. 77ECh. 5.1 - Riemann sums for constant functions Let f(x) = c,...Ch. 5.1 - Prob. 79ECh. 5.1 - Prob. 80ECh. 5.1 - Prob. 81ECh. 5.2 - Suppose f(x) = 5. 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Indefinite integrals Use a change of variables or...Ch. 5.5 - sec2(10x+7)dxCh. 5.5 - Indefinite integrals Use a change of variables or...Ch. 5.5 - Indefinite integrals Use a change of variables or...Ch. 5.5 - Indefinite integrals Use a change of variables or...Ch. 5.5 - Indefinite integrals Use a change of variables or...Ch. 5.5 - Indefinite integrals Use a change of variables or...Ch. 5.5 - Indefinite integrals Use a change of variables or...Ch. 5.5 - Indefinite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - Definite integrals Use a change of variables or...Ch. 5.5 - 0ln4ex3+2exdxCh. 5.5 - 01x1x2dxCh. 5.5 - Prob. 66ECh. 5.5 - Prob. 67ECh. 5.5 - 06/5dx25x2+36Ch. 5.5 - 02x316x4dxCh. 5.5 - 11(x1)(x22x)7dxCh. 5.5 - 0sinx2+cosxdxCh. 5.5 - 01(v+1)(v+2)2v3+9v2+12v+36dvCh. 5.5 - 1249x2+6x+1dxCh. 5.5 - 0/4esin2xsin2xdxCh. 5.5 - Average velocity An object moves in one dimension...Ch. 5.5 - Periodic motion An object moves along a line with...Ch. 5.5 - Population models The population of a culture of...Ch. 5.5 - Variations on the substitution method Evaluate the...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - x(x+10)9dxCh. 5.5 - 033dx9+x2Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Prob. 94ECh. 5.5 - Explain why or why not Determine whether the...Ch. 5.5 - Prob. 96ECh. 5.5 - Prob. 97ECh. 5.5 - Areas of regions Find the area of the following...Ch. 5.5 - Prob. 99ECh. 5.5 - Prob. 100ECh. 5.5 - Substitutions Suppose that p is a nonzero real...Ch. 5.5 - Prob. 102ECh. 5.5 - Average value of sine functions Use a graphing...Ch. 5.5 - Equal areas The area of the shaded region under...Ch. 5.5 - Equal areas The area of the shaded region under...Ch. 5.5 - Prob. 106ECh. 5.5 - Prob. 107ECh. 5.5 - Prob. 108ECh. 5.5 - More than one way Occasionally, two different...Ch. 5.5 - Prob. 110ECh. 5.5 - Prob. 111ECh. 5.5 - sin2 ax and cos2 ax integrals Use the Substitution...Ch. 5.5 - Integral of sin2 x cos2 x Consider the integral...Ch. 5.5 - Substitution: shift Perhaps the simplest change of...Ch. 5.5 - Prob. 115ECh. 5.5 - Prob. 116ECh. 5.5 - Prob. 117ECh. 5.5 - Prob. 118ECh. 5.5 - Multiple substitutions If necessary, use two or...Ch. 5 - Explain why or why not Determine whether the...Ch. 5 - Prob. 2RECh. 5 - Ascent rate of a scuba diver Divers who ascend too...Ch. 5 - Use the tabulated values of f to estimate the...Ch. 5 - Estimate 144x+1dx by evaluating the left, right,...Ch. 5 - Prob. 6RECh. 5 - Estimating a definite integral Use a calculator...Ch. 5 - Suppose the expression lim0k=1n(xk3+xk)xk is the...Ch. 5 - Integration by Riemann sums Consider the integral...Ch. 5 - Limit definition of the definite integral Use the...Ch. 5 - Limit definition of the definite integral Use the...Ch. 5 - Limit definition of the definite integral Use the...Ch. 5 - Prob. 13RECh. 5 - Sum to integral Evaluate the following limit by...Ch. 5 - Symmetry properties Suppose that 04f(x)dx=10 and...Ch. 5 - Properties of integrals The figure shows the areas...Ch. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Area by geometry Use geometry to evaluate the...Ch. 5 - Displacement by geometry Use geometry to find the...Ch. 5 - Area by geometry Use geometry to evaluate...Ch. 5 - Use geometry and properties of integrals to...Ch. 5 - Prob. 27RECh. 5 - Prob. 28RECh. 5 - Evaluate the following derivatives. 29....Ch. 5 - Evaluate the following derivatives....Ch. 5 - Evaluate the following derivatives. 31....Ch. 5 - Evaluate the following derivatives. 32....Ch. 5 - Evaluate the following derivatives. 33....Ch. 5 - Evaluate the following derivatives. 34....Ch. 5 - Find the intervals on which f(x)=x1(t3)(t6)11dt is...Ch. 5 - Area function by geometry Use geometry to find the...Ch. 5 - Given that F=f, use the substitution method to...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - 015re3r2+2drCh. 5 - sinzsin(cosz)dzCh. 5 - ex+exdxCh. 5 - Evaluating integrals Evaluate the following...Ch. 5 - dx14x2Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - 02cos2x6dxCh. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Prob. 71RECh. 5 - 33(511x17+302x13+117x9+303x3+x2)dxCh. 5 - 1x2sin1xdxCh. 5 - (tan1x)51+x2dxCh. 5 - dx(tan1x)(1+x2)Ch. 5 - sin1x1x2dxCh. 5 - x(x+3)10dxCh. 5 - x7x4+1dxCh. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - 2/52/5dxx25x21Ch. 5 - sin2x1+cos2xdx (Hint: sin2x=2sinxcosx.)Ch. 5 - 1010x200x2dxCh. 5 - /2/2(cos2x+cosxsinx3sinx5)dxCh. 5 - 04f(x)dx for f(x)={2x+1ifx33x2+2x8ifx3Ch. 5 - 05|2x8|dxCh. 5 - Prob. 87RECh. 5 - Area of regions Compute the area of the region...Ch. 5 - Prob. 89RECh. 5 - Prob. 90RECh. 5 - Prob. 91RECh. 5 - Area versus net area Find (i) the net area and...Ch. 5 - Gateway Arch The Gateway Arch in St Louis is 630...Ch. 5 - Root mean square The root mean square (or RMS) is...Ch. 5 - Displacement from velocity A particle moves along...Ch. 5 - Velocity to displacement An object travels on the...Ch. 5 - Find the average value of f(x)=e2xon [0, ln 2].Ch. 5 - Average height A baseball is launched into the...Ch. 5 - Average values Integration is not needed. a. Find...Ch. 5 - Prob. 100RECh. 5 - An unknown function Assume f is continuous on [2,...Ch. 5 - Prob. 102RECh. 5 - Prob. 103RECh. 5 - Change of variables Use the change of variables u3...Ch. 5 - Prob. 105RECh. 5 - Area functions and the Fundamental Theorem...Ch. 5 - Limits with integrals Evaluate the following...Ch. 5 - Limits with integrals Evaluate the following...Ch. 5 - Prob. 109RECh. 5 - Area with a parameter Let a 0 be a real number...Ch. 5 - Inverse tangent integral Prove that for nonzero...Ch. 5 - Prob. 112RECh. 5 - Prob. 113RECh. 5 - Exponential inequalities Sketch a graph of f(t) =...Ch. 5 - Equivalent equations Explain why if a function u...Ch. 5 - Unit area sine curve Find the value of c such that...Ch. 5 - Unit area cubic Find the value of c0 such that the...
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