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An inverse tangent identity a. Use derivatives to show that tan¬x + tan(1/x) is constant, for x > 0 and for x < 0. b. Prove that tan¬'x + tan¬'(1/x) = 7/2, for x > 0. c. Prove that tan¬'x + tan¬'(1/x) = -T/2, for x < 0, and SE conclude that tanx + tan¬'(1/x) = {?, if x> 0 -5 ifx < 0.

An inverse tangent identity a. Use derivatives to show that tan¬x + tan(1/x) is constant, for x > 0 and for x < 0. b. Prove that tan¬'x + tan¬'(1/x) = 7/2, for x > 0. c. Prove that tan¬'x + tan¬'(1/x) = -T/2, for x < 0, and SE conclude that tanx + tan¬'(1/x) = {?, if x> 0 -5 ifx < 0.

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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An inverse tangent identity a. Use derivatives to show that tan¬x + tan(1/x) is constant, for x > 0 and for x < 0. b. Prove that tan¬'x + tan¬'(1/x) = 7/2, for x > 0. c. Prove that tan¬'x + tan¬'(1/x) = -T/2, for x < 0, and SE conclude that tanx + tan¬'(1/x) = {?, if x> 0 -5 ifx < 0.
Transcribed Image Text:An inverse tangent identity a. Use derivatives to show that tan¬x + tan(1/x) is constant, for x > 0 and for x < 0. b. Prove that tan¬'x + tan¬'(1/x) = 7/2, for x > 0. c. Prove that tan¬'x + tan¬'(1/x) = -T/2, for x < 0, and SE conclude that tanx + tan¬'(1/x) = {?, if x> 0 -5 ifx < 0.
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