Calculus
5th Edition
ISBN: 9781429241861
Author: Laura Taalman, Peter Kohn
Publisher: W. H. Freeman
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Chapter 4.7, Problem 27S
a.
To determine
To illustrate: The given function A(2) graphically.
b.
To determine
The value of the A(2) and the A(5) function.
c.
To determine
The explicit formula for
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Suppose an oil spill covers a circular area and the radius, r, increases according to the graph shown below where t
represents the number of minutes since the spill was first observed.
Radius (feet)
80
70
60
50
40
30
20
10
0
r
0 10 20 30 40 50 60 70 80 90
Time (minutes)
(a) How large is the circular area of the spill 30 minutes after it was first observed? Give your answer in terms of π.
square feet
(b) If the cost to clean the oil spill is proportional to the square of the diameter of the spill, express the cost, C, as a
function of the radius of the spill, r. Use a lower case k as the proportionality constant.
C(r) =
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increase from 20 feet to 60 feet?
r(60) - r(20)
Or¹(80-30)
r(80) - r(30)
r-1(80) - r−1(30)
r-1(60) - r¹(20)
6. Graph the function f(x)=log3x. Label three points on the graph (one should be the intercept) with
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gave =
g(x) = 8√√x, [8,64]
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Chapter 4 Solutions
Calculus
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- 3. Mary needs to choose between two investments: One pays 5% compounded annually, and the other pays 4.9% compounded monthly. If she plans to invest $22,000 for 3 years, which investment should she choose? How much extra interest will she earn by making the better choice? For all word problems, your solution must be presented in a sentence in the context of the problem.arrow_forward4 πT14 Sin (X) 3 Sin(2x) e dx 1716 S (sinx + cosx) dxarrow_forwardLet g(x) = f(t) dt, where f is the function whose graph is shown. 3 y f(t) MA t (a) At what values of x do the local maximum and minimum values of g occur? Xmin = Xmin = Xmax = Xmax = (smaller x-value) (larger x-value) (smaller x-value) (larger x-value) (b) Where does g attain its absolute maximum value? x = (c) On what interval is g concave downward? (Enter your answer using interval notation.)arrow_forward
- 2. Graph the function f(x)=e* −1. Label three points on the graph (one should be the intercept) with corresponding ordered pairs (round to one decimal place) and label the asymptote with its equation. Write the domain and range of the function in interval notation. Make your graph big enough to see all important features. You may show the final graph only.arrow_forwardansewer both questions in a very detailed manner . thanks!arrow_forwardQuestion Considering the definition of f(x) below, find lim f(x). Select the correct answer below: -56 -44 ○ -35 ○ The limit does not exist. x+6 -2x² + 3x 2 if x-4 f(x) = -x2 -x-2 if -4x6 -x²+1 if x > 6arrow_forward
- Let g(x) = f(t) dt, where f is the function whose graph is shown. y 5 f 20 30 t (a) Evaluate g(x) for x = 0, 5, 10, 15, 20, 25, and 30. g(0) = g(5) = g(10) = g(15) =| g(20) = g(25) = g(30) = (b) Estimate g(35). (Use the midpoint to get the most precise estimate.) g(35) = (c) Where does g have a maximum and a minimum value? minimum x= maximum x=arrow_forwardQuestion Determine lim f(x) given the definition of f(x) below. (If the limit does not exist, enter DNE.) x+6+ -2x²+3x-2 f(x) -2x-1 if x-5 if -−5≤ x ≤ 6 3 if x 6arrow_forwardQuestion Given the following piecewise function, evaluate lim f(x). (If the limit does not exist, enter DNE.) x-3 Provide your answer below: x² + 3x 3 if x-3 f(x) -3 if -3x -2x²+2x-1 6 if x 6arrow_forward
- Question Given the following piecewise function, evaluate lim f(x). x→2 Select the correct answer below: -73 -24 -9 -12 The limit does not exist. 2x f(x) = -2x²-1 if -2x2 3x+2 if x 2arrow_forwardQuestion Given the following piecewise function, evaluate lim f(x). f(x) = x+1- -2x² - 2x 3x-2 2 x² +3 if x-2 if -2< x <1 if x 1 Select the correct answer below: ○ -4 ○ 1 ○ 4 The limit does not exist.arrow_forwardQuestion Given the following piecewise function, evaluate lim →1− f(x). Select the correct answer below: ○ 1 ○ 4 -4 The limit does not exist. -2x² - 2x x 1arrow_forward
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