EBK SINGLE VARIABLE CALCULUS
8th Edition
ISBN: 8220101383693
Author: Stewart
Publisher: Cengage Learning US
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Textbook Question
Chapter 4.4, Problem 62E
Suppose that a volcano is erupting and readings of the rate r(t) at which solid materials are spewed into the atmosphere are given in the table. The time t is measured in seconds and the units for r(t) are tonnes (metric tons) per second.
(a) Give upper and lower estimates for the total quantity Q(6) of erupted materials after six seconds.
(b) Use the Midpoint Rule to estimate Q(6).
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a is done please show b
A homeware company has been approached to manufacture a cake tin in the shape
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illustrated in Figure 1 below, you should assume the top and bottom of the shape
can be represented by semi-circles. The vertical sides of the cake tin have a height of
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Figure 1 - Plan view of the "ghost" cake tin base.
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15. Please solve this and show each and every step please. PLEASE no chatgpt can I have a real person solve it please!! I am stuck. I am doing pratice problems and I do not even know where to start with this. The question is Please compute the indicated functional value.
Chapter 4 Solutions
EBK SINGLE VARIABLE CALCULUS
Ch. 4.1 - Prob. 1ECh. 4.1 - (a) Use six rectangles to find estimates of each...Ch. 4.1 - (a) Estimate the area under the graph of f(x) =...Ch. 4.1 - Prob. 4ECh. 4.1 - (a) Estimate the area under the graph of f(x) = 1...Ch. 4.1 - Prob. 6ECh. 4.1 - Prob. 7ECh. 4.1 - Prob. 8ECh. 4.1 - With a programmable calculator (or a computer), it...Ch. 4.1 - With a programmable calculator (or a computer), it...
Ch. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - The speed of a runner increased steadily during...Ch. 4.1 - Prob. 14ECh. 4.1 - Oil leaked from a tank at a rate of r(t) liters...Ch. 4.1 - Prob. 16ECh. 4.1 - The velocity graph of a braking car is shown. Use...Ch. 4.1 - The velocity graph of a car accelerating from rest...Ch. 4.1 - In someone infected with measles, the virus level...Ch. 4.1 - The table shows the number of people per day who...Ch. 4.1 - Use Definition 2 to find an expression for the...Ch. 4.1 - Prob. 22ECh. 4.1 - Use Definition 2 to find an expression for the...Ch. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - (a) Use Definition 2 to find an expression for the...Ch. 4.1 - Let A be the area under the graph of an increasing...Ch. 4.1 - If A is the area under the curve y = sin x from 0...Ch. 4.1 - (a) Express the area under the curve y = x5 from 0...Ch. 4.1 - (a) Express the area under the curve y = x4 + 5x2...Ch. 4.1 - Prob. 31ECh. 4.1 - (a) Let An be the area of a polygon with n equal...Ch. 4.2 - Evaluate the Riemann sum for f(x)=x1,6x4, with...Ch. 4.2 - If f(x)=cosx0x3/4 evaluate the Riemann sum with n...Ch. 4.2 - If f(x)=x24,0x3, find the Riemann sum with n = 6,...Ch. 4.2 - (a) Find the Riemann sum for f(x)=1/x,1x2, with...Ch. 4.2 - The graph of a function f is given. Estimate...Ch. 4.2 - The graph of g is shown. Estimate 24g(x)dx with...Ch. 4.2 - A table of values of an increasing function f is...Ch. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 - If you have a CAS that evaluates midpoint...Ch. 4.2 - Prob. 14ECh. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Express the limit as a definite integral on the...Ch. 4.2 - Express the limit as a definite integral on the...Ch. 4.2 - Express the limit as a definite integral on the...Ch. 4.2 - Prob. 20ECh. 4.2 - Use the form of the definition of the integral...Ch. 4.2 - Use the form of the definition of the integral...Ch. 4.2 - Use the form of the definition of the integral...Ch. 4.2 - Use the form of the definition of the integral...Ch. 4.2 - Use the form of the definition of the integral...Ch. 4.2 - Prob. 26ECh. 4.2 - Prove that abxdx=b2a22.Ch. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Express the integral as a limit of sums. Then...Ch. 4.2 - Prob. 32ECh. 4.2 - The graph of f is shown. Evaluate each integral by...Ch. 4.2 - The graph of g consists of two straight lines and...Ch. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Prob. 39ECh. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Prob. 41ECh. 4.2 - Give that 0sin4xdx=38, what is 0sin4d?Ch. 4.2 - In Example 4.1.2 we showed that 01x2dx=13. Use...Ch. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - If 28f(x)dx=7.3 and 24f(x)dx=5.9, find 48f(x)dx.Ch. 4.2 - Prob. 49ECh. 4.2 - Prob. 50ECh. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.2 - Prob. 53ECh. 4.2 - Suppose f has absolute minimum value m and...Ch. 4.2 - Prob. 55ECh. 4.2 - Prob. 56ECh. 4.2 - Use the properties of integrals to verify the...Ch. 4.2 - Prob. 58ECh. 4.2 - Prob. 59ECh. 4.2 - Prob. 60ECh. 4.2 - Prob. 61ECh. 4.2 - Prob. 62ECh. 4.2 - Prob. 63ECh. 4.2 - Prob. 64ECh. 4.2 - Prob. 65ECh. 4.2 - Prob. 66ECh. 4.2 - Prob. 67ECh. 4.2 - Prob. 68ECh. 4.2 - Prob. 69ECh. 4.2 - Prob. 70ECh. 4.2 - Prob. 71ECh. 4.2 - Prob. 72ECh. 4.2 - Express the limit as a definite integral. 73....Ch. 4.2 - Prob. 74ECh. 4.2 - Prob. 75ECh. 4.3 - Explain exactly what is meant by the statement...Ch. 4.3 - Prob. 2ECh. 4.3 - Let g(x)=0xf(t)dt, where f is the function whose...Ch. 4.3 - Prob. 4ECh. 4.3 - Sketch the area represented by g(x). Then find...Ch. 4.3 - Prob. 6ECh. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Prob. 8ECh. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Prob. 10ECh. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Prob. 12ECh. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Prob. 16ECh. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Prob. 18ECh. 4.3 - Evaluate the integral. 19. 13(x2+2x4)dxCh. 4.3 - Prob. 20ECh. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Evaluate the integral. 23. 19xdxCh. 4.3 - Prob. 24ECh. 4.3 - Evaluate the integral. 25. /6sindCh. 4.3 - Prob. 26ECh. 4.3 - Evaluate the integral. 27. 01(u+2)(u3)duCh. 4.3 - Prob. 28ECh. 4.3 - Evaluate the integral. 29. 142+x2xdxCh. 4.3 - Prob. 30ECh. 4.3 - Evaluate the integral. 31. /6/2csctcottdtCh. 4.3 - Prob. 32ECh. 4.3 - Prob. 33ECh. 4.3 - Prob. 34ECh. 4.3 - Evaluate the integral. 35. 12v5+3v6v4dvCh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Prob. 40ECh. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Use a graph to give a rough estimate of the area...Ch. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - Use a graph to give a rough estimate of the area...Ch. 4.3 - Prob. 47ECh. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - If f(x)=0x(1t2)cos2tdt, on what interval is f...Ch. 4.3 - On what interval is the curve y=0xt2t2+t+2dt...Ch. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - The Fresnel function S was defined in Example 3...Ch. 4.3 - The sine integral function Si(x)=0xsinttdt is...Ch. 4.3 - Let g(x)=0xf(t)dt, where f is the function whose...Ch. 4.3 - Let g(x)=0xf(t)dt, where f is the function whose...Ch. 4.3 - Prob. 67ECh. 4.3 - Prob. 68ECh. 4.3 - Prob. 69ECh. 4.3 - Prob. 70ECh. 4.3 - Prob. 71ECh. 4.3 - (a) Show that cos(x2) cos x for 0 x 1. (b)...Ch. 4.3 - Show that 0510x2x4+x2+1dx0.1 by comparing the...Ch. 4.3 - Let f(x)={0ifx0xif0x12xif1x20ifx2 and...Ch. 4.3 - Find a function f and a number a such that...Ch. 4.3 - Prob. 76ECh. 4.3 - A manufacturing company owns a major piece of...Ch. 4.3 - A high-tech company purchases a new computing...Ch. 4.3 - Evaluate the integral. 79. 1912xdxCh. 4.3 - Prob. 80ECh. 4.3 - Prob. 81ECh. 4.3 - Prob. 82ECh. 4.3 - Prob. 83ECh. 4.3 - Prob. 84ECh. 4.4 - Verify by differentiation that the formula is...Ch. 4.4 - Verify by differentiation that the formula is...Ch. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Find the general indefinite integral. 5....Ch. 4.4 - Prob. 6ECh. 4.4 - Find the general indefinite integral. 7....Ch. 4.4 - Prob. 8ECh. 4.4 - Find the general indefinite integral. 9....Ch. 4.4 - Prob. 10ECh. 4.4 - Find the general indefinite integral. 11. 1+x+xxdxCh. 4.4 - Prob. 12ECh. 4.4 - Find the general indefinite integral. 13....Ch. 4.4 - Prob. 14ECh. 4.4 - Find the general indefinite integral. 15....Ch. 4.4 - Prob. 16ECh. 4.4 - Find the general indefinite integral. Illustrate...Ch. 4.4 - Prob. 18ECh. 4.4 - Evaluate the integral. 19. 23(x23)dxCh. 4.4 - Prob. 20ECh. 4.4 - Evaluate the integral. 21. 20(12t4+14t3t)dtCh. 4.4 - Prob. 22ECh. 4.4 - Evaluate the integral. 23. 02(2x3)(4x2+1)dxCh. 4.4 - Prob. 24ECh. 4.4 - Evaluate the integral. 25. 0(4sin3cos)dCh. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - Prob. 34ECh. 4.4 - Prob. 35ECh. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - Prob. 40ECh. 4.4 - Prob. 41ECh. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - Repeat Exercise 43 for the curve y = 2x + 3x4 ...Ch. 4.4 - The area of the region that lies to the right of...Ch. 4.4 - Prob. 46ECh. 4.4 - If w'(t) is the rate of growth of a child in...Ch. 4.4 - Prob. 48ECh. 4.4 - If oil leaks from a tank at a rate of r(t) gallons...Ch. 4.4 - A honeybee population starts with 100 bees and...Ch. 4.4 - In Section 3.7 we defined the marginal revenue...Ch. 4.4 - Prob. 52ECh. 4.4 - If x is measured in meters and f(x) is measured in...Ch. 4.4 - If the units for x are feet and the units for a(x)...Ch. 4.4 - The velocity function (in meters per second) is...Ch. 4.4 - The velocity function (in meters per second) is...Ch. 4.4 - Prob. 57ECh. 4.4 - Prob. 58ECh. 4.4 - The linear density of a rod of length 4 m is given...Ch. 4.4 - Water flows from the bottom of a storage tank at a...Ch. 4.4 - Prob. 61ECh. 4.4 - Suppose that a volcano is erupting and readings of...Ch. 4.4 - Prob. 63ECh. 4.4 - Prob. 64ECh. 4.4 - The graph of the acceleration a(t) of a car...Ch. 4.4 - Shown is the graph of traffic on an Internet...Ch. 4.4 - The following graph shows the power consumption in...Ch. 4.4 - Prob. 68ECh. 4.4 - Evaluate the integral. 69. (sinx+sinhx)dxCh. 4.4 - Prob. 70ECh. 4.4 - Prob. 71ECh. 4.4 - Prob. 72ECh. 4.4 - Prob. 73ECh. 4.4 - The area labeled B is three times the area labeled...Ch. 4.5 - Evaluate the integral by making the given...Ch. 4.5 - Prob. 2ECh. 4.5 - Evaluate the integral by making the given...Ch. 4.5 - Prob. 4ECh. 4.5 - Evaluate the integral by making the given...Ch. 4.5 - Prob. 6ECh. 4.5 - Evaluate the indefinite integral. 7. x1x2dxCh. 4.5 - Prob. 8ECh. 4.5 - Evaluate the indefinite integral. 9. (12x)9dxCh. 4.5 - Prob. 10ECh. 4.5 - Evaluate the indefinite integral. 11. sin(2/3)dCh. 4.5 - Prob. 12ECh. 4.5 - Evaluate the indefinite integral. 13. sec3ttan3tdtCh. 4.5 - Prob. 14ECh. 4.5 - Evaluate the indefinite integral. 15. cos(1+5t)dtCh. 4.5 - Prob. 16ECh. 4.5 - Evaluate the indefinite integral. 17. sec2tan3dCh. 4.5 - Prob. 18ECh. 4.5 - Evaluate the indefinite integral. 19....Ch. 4.5 - Prob. 20ECh. 4.5 - Prob. 21ECh. 4.5 - Evaluate the indefinite integral. 22. cos(/x)x2dxCh. 4.5 - Evaluate the indefinite integral. 23. z21+z33dzCh. 4.5 - Prob. 24ECh. 4.5 - Evaluate the indefinite integral. 25. cotxcsc2xdxCh. 4.5 - Prob. 26ECh. 4.5 - Evaluate the indefinite integral. 27. sec3xtanxdxCh. 4.5 - Prob. 28ECh. 4.5 - Evaluate the indefinite integral. 29. x(2x+5)8dxCh. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Prob. 32ECh. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Evaluate the definite integral. 35. 01cos(t/2)dtCh. 4.5 - Prob. 36ECh. 4.5 - Evaluate the definite integral. 37. 011+7x3dxCh. 4.5 - Prob. 38ECh. 4.5 - Prob. 39ECh. 4.5 - Prob. 40ECh. 4.5 - Prob. 41ECh. 4.5 - Prob. 42ECh. 4.5 - Evaluate the definite integral. 43. 013dx(1+2x)23Ch. 4.5 - Prob. 44ECh. 4.5 - Evaluate the definite integral. 45. 0axx2+a2dx(a0)Ch. 4.5 - Prob. 46ECh. 4.5 - Evaluate the definite integral. 47. 12xx1dxCh. 4.5 - Prob. 48ECh. 4.5 - Evaluate the definite integral. 49....Ch. 4.5 - Prob. 50ECh. 4.5 - Prob. 51ECh. 4.5 - Prob. 52ECh. 4.5 - Use a graph to give a rough estimate of the area...Ch. 4.5 - Use a graph to give a rough estimate of the area...Ch. 4.5 - Prob. 55ECh. 4.5 - Prob. 56ECh. 4.5 - Breathing is cyclic and a full respiratory cycle...Ch. 4.5 - A model for the basal metabolism rate, in kcal/h,...Ch. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Prob. 61ECh. 4.5 - Prob. 62ECh. 4.5 - If a and b are positive numbers, show that...Ch. 4.5 - If f is continuous on [0, ], use the substitution...Ch. 4.5 - If f is continuous, prove that...Ch. 4.5 - Prob. 66ECh. 4.5 - Prob. 67ECh. 4.5 - Prob. 68ECh. 4.5 - Prob. 69ECh. 4.5 - Prob. 70ECh. 4.5 - Prob. 71ECh. 4.5 - Prob. 72ECh. 4.5 - Prob. 73ECh. 4.5 - Prob. 74ECh. 4.5 - Prob. 75ECh. 4.5 - Evaluate the integral. 76. sin(lnx)xdxCh. 4.5 - Prob. 77ECh. 4.5 - Prob. 78ECh. 4.5 - Prob. 79ECh. 4.5 - Prob. 80ECh. 4.5 - Prob. 81ECh. 4.5 - Prob. 82ECh. 4.5 - Evaluate the integral. 83. 01ez+1ez+zdzCh. 4.5 - Prob. 84ECh. 4.5 - Prob. 85ECh. 4 - (a) Write an expression for a Riemann sum of a...Ch. 4 - (a) Write the definition of the definite integral...Ch. 4 - State the Midpoint Rule.Ch. 4 - State both parts of the Fundamental Theorem of...Ch. 4 - (a) State the Net Change Theorem. (b) If r(t) is...Ch. 4 - Suppose a particle moves back and forth along a...Ch. 4 - Prob. 7RCCCh. 4 - Explain exactly what is meant by the statement...Ch. 4 - Prob. 9RCCCh. 4 - Prob. 1RQCh. 4 - Prob. 2RQCh. 4 - Prob. 3RQCh. 4 - Prob. 4RQCh. 4 - Prob. 5RQCh. 4 - Prob. 6RQCh. 4 - Prob. 7RQCh. 4 - Prob. 8RQCh. 4 - Prob. 9RQCh. 4 - Determine whether the statement is true or false....Ch. 4 - Prob. 11RQCh. 4 - Prob. 12RQCh. 4 - Prob. 13RQCh. 4 - Prob. 14RQCh. 4 - Prob. 15RQCh. 4 - Prob. 16RQCh. 4 - Prob. 17RQCh. 4 - Determine whether the statement is true or false....Ch. 4 - Use the given graph of f to find the Riemann sum...Ch. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - The figure shows the graphs of f,f, and 0xf(t)dt....Ch. 4 - Evaluate: (a) 0/2ddx(sinx2cosx3)dx (b)...Ch. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - A particle moves along a line with velocity...Ch. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - A population of honeybees increased at a rate of...Ch. 4 - Prob. 50RECh. 4 - If f is continuous and 02f(x)dx=6, evaluate...Ch. 4 - The Fresnel function S(x)=0xsin(12t2)dt was...Ch. 4 - Prob. 53RECh. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - Prob. 56RECh. 4 - If f is continuous on [0, 1], prove that...Ch. 4 - Prob. 58RECh. 4 - Prob. 1PCh. 4 - Prob. 2PCh. 4 - Prob. 3PCh. 4 - (a) Graph several members of the family of...Ch. 4 - Prob. 5PCh. 4 - If f(x)=0xx2sin(t2)dt, find f(x).Ch. 4 - Prob. 7PCh. 4 - Prob. 8PCh. 4 - Prob. 9PCh. 4 - Find d2dx20x(1sint1+u4du)dt.Ch. 4 - Suppose the coefficients of the cubic polynomial...Ch. 4 - Prob. 12PCh. 4 - Prob. 13PCh. 4 - The figure shows a parabolic segment, that is. a...Ch. 4 - Prob. 15PCh. 4 - Prob. 16PCh. 4 - Evaluate limn(1nn+1+1nn+2++1nn+n).Ch. 4 - For any number c, we let fc(x) be the smaller of...
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The average velocity over the interval [1,5] is Vav = (Simplify your answer.)arrow_forwardFor the position function s(t) = - 16t² + 105t, complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t = 1. Time Interval Average Velocity [1,2] Complete the following table. Time Interval Average Velocity [1, 1.5] [1, 1.1] [1, 1.01] [1, 1.001] [1,2] [1, 1.5] [1, 1.1] [1, 1.01] [1, 1.001] ப (Type exact answers. Type integers or decimals.) The value of the instantaneous velocity at t = 1 is (Round to the nearest integer as needed.)arrow_forwardFind the following limit or state that it does not exist. Assume b is a fixed real number. (x-b) 40 - 3x + 3b lim x-b x-b ... Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (x-b) 40 -3x+3b A. lim x-b x-b B. The limit does not exist. (Type an exact answer.)arrow_forwardx4 -289 Consider the function f(x) = 2 X-17 Complete parts a and b below. a. Analyze lim f(x) and lim f(x), and then identify the horizontal asymptotes. x+x X--∞ lim 4 X-289 2 X∞ X-17 X - 289 lim = 2 ... X∞ X - 17 Identify the horizontal asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. A. The function has a horizontal asymptote at y = B. The function has two horizontal asymptotes. The top asymptote is y = and the bottom asymptote is y = ☐ . C. The function has no horizontal asymptotes. b. Find the vertical asymptotes. For each vertical asymptote x = a, evaluate lim f(x) and lim f(x). Select the correct choice and, if necessary, fill in the answer boxes to complete your choice. earrow_forwardExplain why lim x²-2x-35 X-7 X-7 lim (x+5), and then evaluate lim X-7 x² -2x-35 x-7 x-7 Choose the correct answer below. A. x²-2x-35 The limits lim X-7 X-7 and lim (x+5) equal the same number when evaluated using X-7 direct substitution. B. Since each limit approaches 7, it follows that the limits are equal. C. The numerator of the expression X-2x-35 X-7 simplifies to x + 5 for all x, so the limits are equal. D. Since x²-2x-35 X-7 = x + 5 whenever x 7, it follows that the two expressions evaluate to the same number as x approaches 7. Now evaluate the limit. x²-2x-35 lim X-7 X-7 = (Simplify your answer.)arrow_forwardA function f is even if f(x) = f(x) for all x in the domain of f. If f is even, with lim f(x) = 4 and x-6+ lim f(x)=-3, find the following limits. X-6 a. lim f(x) b. +9-←x lim f(x) X-6 a. lim f(x)= +9-←x (Simplify your answer.) b. lim f(x)= X→-6 (Simplify your answer.) ...arrow_forwardEvaluate the following limit. lim X-X (10+19) Select the correct answer below and, if necessary, fill in the answer box within your choice. 10 A. lim 10+ = 2 ☐ (Type an integer or a simplified fraction.) X-∞ B. 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