(a) Explanation Given information: The function y = tan x , the point ( 0 , 0 ) , and the interval − π 2 < x < π 2 . Explanation: The equation of the line passing through point ( x 1 , y 1 ) is given by the formula y - y 1 = m ( x - x 1 ) , where m is the slope of the line. First find the slope to the tangent line to y = tan x at ( 0 , 0 ) , then, find thederivative of the given function. ⇒ d y d x | x = 0 = [ d d x ( tan x ) ] x = 0 ⇒ d y d x | x = 0 = sec 2 x | x = 0 By substituting x = 0 , ⇒ d y (b) To determine To graph: The function y = tan x in the interval − π 2 < x < π 2 and draw the tangent line at point ( 0 , 0 ) .

Calculus & Its Applications (14th Edition)

14th Edition

ISBN: 9780134437774

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar

Publisher: PEARSON

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Chapter 8.4, Problem 34E

(a)

To determine

The equation of thetangent line to the graph of y = tan x at point (0, 0).

(b)

To determine

To graph: The function y = tan x in the interval − π2 < x < π2 and draw the tangent line at point (0, 0).

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Chapter 8.4, Problem 33E

Chapter 8.4, Problem 35E

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Chapter 8 Solutions

Calculus & Its Applications (14th Edition)

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The equation of thetangent line to the graph of y = tan x at point ( 0 , 0 ) .

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The equation of thetangent line to the graph of y = tan x at point (0, 0).

To graph: The function y = tan x in the interval − π2 < x < π2 and draw the tangent line at point (0, 0).

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Chapter 8 Solutions