Concept explainers
(a)
To sketch the graph of ln(x).
(a)
Explanation of Solution
Given information:
Given
Graph:
The value of
The graph of ln(x) is given below as,
(b)
To sketch the graph of
(b)
Explanation of Solution
Given information:
Given
Graph:
The value of
The graph of
(c)
To sketch:The graph of
(c)
Explanation of Solution
Given information:
Given
Graph:
The value of
The graph of
(d)
To calculate: sketch the graph of
(d)
Answer to Problem 71E
The graph of
Explanation of Solution
Given information:
Given
Calculation:
The value of
The graph of
(e)
To calculate: sketch the graph of
(e)
Answer to Problem 71E
The graph of
Explanation of Solution
Given information:
Given
Calculation:
The value of
The graph of
(f)
To calculate: sketch the graph of
(f)
Answer to Problem 71E
The graph of
Explanation of Solution
Given information:
Given
Calculation:
The value of
The graph of
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Chapter 1 Solutions
Modeling the Dynamics of Life: Calculus and Probability for Life Scientists
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- Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.arrow_forwardRepeat the previous exercise to find the formula forthe APY of an account that compounds daily. Usethe results from this and the previous exercise todevelop a function I(n)for the APY of any accountthat compounds n times per year.arrow_forwardIf the instantaneous rate of change of f(x) with respect to x is positive when x=1, is f increasing or decreasing there ?arrow_forward
- The natural logarithmic function f(x)=Inx has the ____________ asymptote x =____.arrow_forwardThis exercise shows another way to derive the formula for the derivative of the natural logarithm function using the definition of the derivative. a. Using the definition of the derivative, show that d(lnx)dx=limh0ln(1+hx)1h. b. Eliminate h from the result in part a using the substitution h=x/m to show that d(lnx)dx=limmln[(1+1m)m]1/x c. What property should the function g have that would yield limmg(h(m))=g(limmh(m))? Assuming that the natural logarithm has this property, and using the result about (1+1/m)m from Section 2.1, show that d(lnx)dx=lne1/x=1x.arrow_forward
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