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2. COMPUTING LIMITS AND DERIVATIVES: (a) At what r value is the slope of the graph of f(x) = 3xª + x² equal to -1.7? (b) Find (0.7+ h)° – 0.7° lim h→0 h in the following two ways: i. Use your calculator to compute the limit. ii. Notice that the limit you are being asked to compute is the limit as h 0 of the difference quotient of some function at some point. Namely, the limit equals f'(c) for some function f (x) and some real number c. Find this function, and the value of c (no calculations are needed here, just look carefully at the expression in the limit). Then, use your calculator to differentiate this function and evaluate the derivative at r = c. Calculator Tips: For a video tutorial on computing limits with a calculator, click here. Towards the end, the video shows how to find one-sided limits, which may also be useful. The textbook also has instructions at the end of section 2.3 (pg. 218-219). For a video tutorial on finding derivatives using a calculator, click here. For instructions in the textbook, see section 2.2 (pg. 202).

2. COMPUTING LIMITS AND DERIVATIVES: (a) At what r value is the slope of the graph of f(x) = 3xª + x² equal to -1.7? (b) Find (0.7+ h)° – 0.7° lim h→0 h in the following two ways: i. Use your calculator to compute the limit. ii. Notice that the limit you are being asked to compute is the limit as h 0 of the difference quotient of some function at some point. Namely, the limit equals f'(c) for some function f (x) and some real number c. Find this function, and the value of c (no calculations are needed here, just look carefully at the expression in the limit). Then, use your calculator to differentiate this function and evaluate the derivative at r = c. Calculator Tips: For a video tutorial on computing limits with a calculator, click here. Towards the end, the video shows how to find one-sided limits, which may also be useful. The textbook also has instructions at the end of section 2.3 (pg. 218-219). For a video tutorial on finding derivatives using a calculator, click here. For instructions in the textbook, see section 2.2 (pg. 202).

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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2. COMPUTING LIMITS AND DERIVATIVES: (a) At what a value is the slope of the graph of f(x) = 3x + x² equal to -1.7? %3D (b) Find (0.7+ h)° – 0.7 lim h→0 in the following two ways: i. Use your calculator to compute the limit. ii. Notice that the limit you are being asked to compute is the limit as h 0 of the difference quotient of some function at some point. Namely, the limit equals f'(c) for some function f(x) and some real number c. Find this function, and the value of c (no calculations are needed here, just look carefully at the expression in the limit). Then, use your calculator to differentiate this function and evaluate the derivative at x = c. Calculator Tips: For a video tutorial on computing limits with a calculator, click here. Towards the end, the video shows how to find one-sided limits, which may also be useful. The textbook also has instructions at the end of section 2.3 (pg. 218-219). For a video tutorial on finding derivatives using a calculator, click here. For instructions in the textbook, see section 2.2 (pg. 202).
Transcribed Image Text:2. COMPUTING LIMITS AND DERIVATIVES: (a) At what a value is the slope of the graph of f(x) = 3x + x² equal to -1.7? %3D (b) Find (0.7+ h)° – 0.7 lim h→0 in the following two ways: i. Use your calculator to compute the limit. ii. Notice that the limit you are being asked to compute is the limit as h 0 of the difference quotient of some function at some point. Namely, the limit equals f'(c) for some function f(x) and some real number c. Find this function, and the value of c (no calculations are needed here, just look carefully at the expression in the limit). Then, use your calculator to differentiate this function and evaluate the derivative at x = c. Calculator Tips: For a video tutorial on computing limits with a calculator, click here. Towards the end, the video shows how to find one-sided limits, which may also be useful. The textbook also has instructions at the end of section 2.3 (pg. 218-219). For a video tutorial on finding derivatives using a calculator, click here. For instructions in the textbook, see section 2.2 (pg. 202).
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