Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem , and some problems will require more than one application of L’Hôpital’s rule. 58 . lim x → ∞ ln ( 1 + 2 e − x ) ln ( 1 + e − x )
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem , and some problems will require more than one application of L’Hôpital’s rule. 58 . lim x → ∞ ln ( 1 + 2 e − x ) ln ( 1 + e − x )
Solution Summary: The author evaluates the value of the limit undersetxto.
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule.
In Problems 43–66, find the indicated extremum of each function
on the given interval.
1. In the figure below, find the number(s) "c" that
Rolle's Theorem promises (guarantees).
10
For Problems 2–4, verify that the hypotheses of
Rolle's Theorem are satisfied for each of the func-
tions on the given intervals, and find the value of
the number(s) "c" that Rolle's Theorem promises.
2. (a) f(x) = x² on |-2, 2
(b) f(x) = x² =5x +8 on [0,5]
3. (a) f(x) = sin(x) on [0, 7]
(b) f(x) = sin(x) on [A,57]|
4. (a) f(x) = r-x+3 on | 1,1]
(b) f(x) = x cos(x) on (0,
[0, 1
In Problems 85–90, use the Intermediate Value Theorem to show that each function has a zero in the given interval. Approximate the zerocorrect to two decimal places.
Chapter 4 Solutions
Additional Calculus Topics for Calculus for Business, Economics, Life Sciences and Social Sciences
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.