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Problem 14.4. Use Taylor polynomials in order to approximate the functions and calculate the following limits: 47 – 1 lim z-0 7 - 1 (14.23) In(1+1) – I 40 1-r? cos(r) (14.24) lim

Problem 14.4. Use Taylor polynomials in order to approximate the functions and calculate the following limits: 47 – 1 lim z-0 7 - 1 (14.23) In(1+1) – I 40 1-r? cos(r) (14.24) lim

Calculus: Early Transcendentals
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. Attached is the JPG file with my Calculus questions.

**Problem 14.4**: Use Taylor polynomials in order to approximate the functions and calculate the following limits: 1. \((14.23)\) \(\lim_{{x \to 0}} \frac{{4^x - 1}}{{7x - 1}}\) 2. \((14.24)\) \(\lim_{{x \to 0}} \frac{{\ln(1 + x) - x}}{{1 - x^2 \cos(x)}}\) In this problem, you'll apply Taylor series expansions to approximate the given functions as \(x\) approaches 0 and calculate the specified limits. Taylor polynomials are useful for simplifying complex functions around a specific point, allowing easier limit calculations.
Transcribed Image Text:**Problem 14.4**: Use Taylor polynomials in order to approximate the functions and calculate the following limits: 1. \((14.23)\) \(\lim_{{x \to 0}} \frac{{4^x - 1}}{{7x - 1}}\) 2. \((14.24)\) \(\lim_{{x \to 0}} \frac{{\ln(1 + x) - x}}{{1 - x^2 \cos(x)}}\) In this problem, you'll apply Taylor series expansions to approximate the given functions as \(x\) approaches 0 and calculate the specified limits. Taylor polynomials are useful for simplifying complex functions around a specific point, allowing easier limit calculations.
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