19. Using the l’Hospital's rule to find the limitse3 – 1In(In x)e – 1– x – ²(а) lim-0 In(x + 1)(b) lim(c) lim(d) lim1In x20. [The l'Hospital's rule.](a) Find the limit lim x ln (1 + !), and then show that lim (1+ !)ª == e.Application: Suppose an amount of $1 is invested in the bank, with continuous compoundingof interest at interest rate 100% (r = 1), find the the amount after 1 year.(b) Find lim (1+ )*,3x(c) lim x Inx,(d) lim x".

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Answered: 19. Using the l'Hospital's rule to find…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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1. Broadly speaking, what are the Limit Laws, and why do they help us calculate limits?2. In Example 3, there is a step where the function x2 − 1x − 1is changed to x+ 1. But unlike the secondfunction, the first function is undefined at x = 1. How can we justify changing functions this way?3. Explain the flaw in the following calculation:limx→0x2sin(1/x) = (limx→0x2) · (limx→0sin(1/x)) = 0 · (limx→0sin(1/x)) = 0.
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19. Using the l'Hospital's rule to find the limits e3r – 1 In(ln æ) 1 e" – 1- x – ² (a) lim a→0 In(x + 1) (b) lim (c) lim (d) lim 1 In x