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36. g(x) = ex²-x

36. g(x) = ex²-x

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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Question 36
### Limits and Differentiation in Calculus #### Exercises on Limit Calculation: **21.** Compare the functions \( f(x) = x^{10} \) and \( g(x) = e^x \) by graphing both \( f \) and \( g \) in several viewing rectangles. Analyze when the graph of \( g \) finally surpasses the graph of \( f \). **22.** Use a graph to estimate the value of \( x \) such that \( e^x > 1,000,000,000.00 \). ##### Find the Limit: **23.** \(\lim_{{x \to 0}} (1.001)^x\) **24.** \(\lim_{{x \to \infty}} (1.001)^x\) **25.** \(\lim_{{x \to \infty}} \frac{e^{3x} - e^{-3x}}{e^{3x} + e^{-3x}}\) **26.** \(\lim_{{x \to -x^2}} e^{3/(2-x)}\) **27.** \(\lim_{{x \to 2^+}} e^{3/(2-x)}\) **28.** \(\lim_{{x \to 2^-}} e^{3/(2-x)}\) **29.** \(\lim_{{x \to \infty}} \left(e^{-2x} \cos x\right)\) **30.** \(\lim_{{x \to (\pi/2)^+}} e^{\tan x}\) #### Exercises on Differentiation: **31.** Differentiate the function \( f(x) = e^5 \). **32.** \( k(r) = e^r + r^e \) **33.** \( f(x) = (3x^2 - 5x)e^x \) **34.** \( y = \frac{e^x}{1 - e^x} \) **35.** \( y = e^{ax^3} \) **36.** \( g(x) = e^{x^2 - x} \) **37.** \( y = e^{\tan \theta} \) **38.** \( V(t) = \frac{4 + t}{te
Transcribed Image Text:### Limits and Differentiation in Calculus #### Exercises on Limit Calculation: **21.** Compare the functions \( f(x) = x^{10} \) and \( g(x) = e^x \) by graphing both \( f \) and \( g \) in several viewing rectangles. Analyze when the graph of \( g \) finally surpasses the graph of \( f \). **22.** Use a graph to estimate the value of \( x \) such that \( e^x > 1,000,000,000.00 \). ##### Find the Limit: **23.** \(\lim_{{x \to 0}} (1.001)^x\) **24.** \(\lim_{{x \to \infty}} (1.001)^x\) **25.** \(\lim_{{x \to \infty}} \frac{e^{3x} - e^{-3x}}{e^{3x} + e^{-3x}}\) **26.** \(\lim_{{x \to -x^2}} e^{3/(2-x)}\) **27.** \(\lim_{{x \to 2^+}} e^{3/(2-x)}\) **28.** \(\lim_{{x \to 2^-}} e^{3/(2-x)}\) **29.** \(\lim_{{x \to \infty}} \left(e^{-2x} \cos x\right)\) **30.** \(\lim_{{x \to (\pi/2)^+}} e^{\tan x}\) #### Exercises on Differentiation: **31.** Differentiate the function \( f(x) = e^5 \). **32.** \( k(r) = e^r + r^e \) **33.** \( f(x) = (3x^2 - 5x)e^x \) **34.** \( y = \frac{e^x}{1 - e^x} \) **35.** \( y = e^{ax^3} \) **36.** \( g(x) = e^{x^2 - x} \) **37.** \( y = e^{\tan \theta} \) **38.** \( V(t) = \frac{4 + t}{te
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