   Chapter 11.1, Problem 72E

Chapter
Section
Textbook Problem

# Finding Unit VectorsIn Exercises 67–72, find a unit vector (a) parallel to and (b) perpendicular to the graph of f at the given point. Then sketch the graph of f and sketch the vectors at the given point. f ( x ) = tan x ,     ( π 4 , 1 )

To determine
A Unit vector parallel to and perpendicular to f(x)=tanx,  (π4,1).

Explanation

Given: f(x)=tanx,  (π4,1)

Explanation: Differentiate with respect to x, f'(x)=sec2x     [As ddxtanx=sec2x]f'(π4)=sec2π4=2   [As secπ4=2]Now slop is 2 yx=2   y

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