34. DISCUSS: Graphing Calculator Pitfalls (a) Evaluate tan x - x h(x) : for x = 1, 0.5, 0.1, 0.05, 0.01, and 0.005. tan x - x (b) Guess the value of lim (c) Evaluate h(x) for successively smaller values of x until you finally get a value of 0 for h(x). Are you still confident that your guess in part (b) is correct? Explain why you eventually got a value of 0 for h(x). (d) Graph the function h in the viewing rectangle [–1, 1] by [0, 1]. Then zoom in toward the point where the graph crosses the y-axis to estimate the limit of h(x) as x approaches 0. Continue to zoom in until you observe dis- tortions in the graph of h. Compare with your results in part (c).
34. DISCUSS: Graphing Calculator Pitfalls (a) Evaluate tan x - x h(x) : for x = 1, 0.5, 0.1, 0.05, 0.01, and 0.005. tan x - x (b) Guess the value of lim (c) Evaluate h(x) for successively smaller values of x until you finally get a value of 0 for h(x). Are you still confident that your guess in part (b) is correct? Explain why you eventually got a value of 0 for h(x). (d) Graph the function h in the viewing rectangle [–1, 1] by [0, 1]. Then zoom in toward the point where the graph crosses the y-axis to estimate the limit of h(x) as x approaches 0. Continue to zoom in until you observe dis- tortions in the graph of h. Compare with your results in part (c).
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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