Evaluating Functions Evaluate the function at theindicated values.19. f(x) = x² – 6; f(-3). f(3), f(0), f(20. f(x) = x' + 2x; f(-2), f(-1), f(0), f(!)

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 1E

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Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.
Maximum Sales Growth This is a continuation of Exercise 10. In this exercise, we determine how the sales level that gives the maximum growth rate is related to the limit on sales. Assume, as above, that the constant of proportionality is 0.3, but now suppose that sales grow to a level of 4 thousand dollars in the limit. a. Write an equation that shows the proportionality relation for G. b. On the basis of the equation from part a, make a graph of G as a function of s. c. At what sales level is the growth rate as large as possible? d. Replace the limit of 4 thousand dollars with another number, and find at what sales level the growth rate is as large as possible. What is the relationship between the limit and the sales level that gives the largest growth rate? Does this relationship change if the proportionality constant is changed? e. Use your answers in part d to explain how to determine the limit if we are given sales data showing the sales up to a point where the growth rate begins to decrease.
Filling in a function value The domain of ƒ(x, y) = e-1/(x2 + y2) excludes (0, 0). How should ƒ be defined at (0, 0) to make it continuous there?
Identifying homogenous or non homogenous functions. Show your complete solution. when x=0, y=3 xy3dx+ex^2dy=0
F(x)=x^3+x+1 Find where it increasing/ decreasing and the maximum and minimum values
Using linear approximation to estimate f(3.2)-f(3) for f(x)8/(1+x^2)
The participation rate is the number of people in the labor force divided by the civilian population (excludes military). Let L(x) represent the size of thelabor force in year x, and P(x) represent the civilian population in year x. Determine a function that represents the participation rate R as a function of x.
h(x) = 4/((x-1)^2) Show from the definition that the function h(x) = 4/((x-1)^2) is increasing in the interval (-∞, 1) and decreasing in the interval (1,+∞).
The behavior of a function f (x) can be discovered by studying the sign of its derivative f´ (x). For example: Se f´(x) > 0 in ] a ,b [ then f(x) é increasing in ] a, b [.Se f´(x) < 0 in ] a, b [ then f(x) é decreasing in ] a, b [. If f´ (x) = 0 at a given point P then f (x) has a critical point (maximum, minimum or inflection) in P. Analyze the graphs below, indicate which function [a (x), b (x) or c (x)], the function f (x) is the derivative of. Justify your choice. I have no idea how can i pass by that. If someone can help me, i'l be so thankful.
Higher-order derivatives Find ƒ′(x), ƒ″(x), and ƒ‴(x) for thefollowing functions.
Use derivatives to find the critical points and inflection points. f(x)=5x - 2lnxEnter the exact answers in increasing order. If there is only one critical point, enter NA in the second area. If there are no inflection points, enter NA
Find all critical points where the second derivative equals zero or does not exist for the functions below.Label the intervals of increase and decrease based on the first derivative and intervals of concavity based on the second derivative. Deterime your local extrema and you inflection points, and list both coordinates of each. 1. f(x)=4/(x2+4)

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Evaluating Functions Evaluate the function at the indicated values. 19. f(x) = x² – 6; f(-3). f(3), f(0), f( 20. f(x) = x' + 2x; f(-2), f(-1), f(0), f(!)