Problem 14.4. Use Taylor polynomials in order to approximate the functions and calculate the following limits: sin(8x) lim x→0 sin(7x) (14.20) sin(x) – x lim - (14.21) In(1+ x) lim x→0 e5x (14.22) 1 1
Problem 14.4. Use Taylor polynomials in order to approximate the functions and calculate the following limits: sin(8x) lim x→0 sin(7x) (14.20) sin(x) – x lim - (14.21) In(1+ x) lim x→0 e5x (14.22) 1 1
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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Hi, I hope you are doing well. I have some questions in the attached JPG file where I need to use Taylor polynomials to find the limit.
![**Problem 14.4.** Use Taylor polynomials in order to approximate the functions and calculate the following limits:
\( (14.20) \)
\[
\lim_{x \to 0} \frac{\sin(8x)}{\sin(7x)}
\]
\( (14.21) \)
\[
\lim_{x \to 0} \frac{\sin(x) - x}{x^5}
\]
\( (14.22) \)
\[
\lim_{x \to 0} \frac{\ln(1 + x)}{e^{5x} - 1}
\]
\( (14.23) \)
\[
\lim_{x \to 0} \frac{4^x - 1}{7x - 1}
\]
\( (14.24) \)
\[
\lim_{x \to 0} \frac{\ln(1 + x) - x}{1 - x^2 \cos(x)}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5111351b-1042-4886-8af2-a2d624148dd8%2F80753445-4c24-4599-98f6-c80061af7faf%2Ftu3j4mj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 14.4.** Use Taylor polynomials in order to approximate the functions and calculate the following limits:
\( (14.20) \)
\[
\lim_{x \to 0} \frac{\sin(8x)}{\sin(7x)}
\]
\( (14.21) \)
\[
\lim_{x \to 0} \frac{\sin(x) - x}{x^5}
\]
\( (14.22) \)
\[
\lim_{x \to 0} \frac{\ln(1 + x)}{e^{5x} - 1}
\]
\( (14.23) \)
\[
\lim_{x \to 0} \frac{4^x - 1}{7x - 1}
\]
\( (14.24) \)
\[
\lim_{x \to 0} \frac{\ln(1 + x) - x}{1 - x^2 \cos(x)}
\]
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