(a) Show that lim x/2(/2 x)tan x = 1.(b) Show thatlimx/2 1/2 x tan x= 0(c) It follows

Chapter 3, Problem 64

(choose chapter or problem)

(a) Show that \(\lim _{x \rightarrow \pi / 2}(\pi / 2-x) \tan x=1\)
(b) Show that

\(\lim _{x \rightarrow \pi / 2}\left(\frac{1}{\pi / 2-x}-\tan x\right)=0\)

(c) It follows from part (b) that the approximation \(\tan x \approx \frac{1}{\pi / 2-x}\)should be good for values of x near \(\pi / 2\). Use a calculator to find tanx and \(1 /(\pi / 2-x)\) for \(x=1.57\) ; compare the results.

Equation Transcription:

Text Transcription:

lim _x right arrow pi/2 (pi/2-x)tanx=1

lim _x right arrow pi/2 (1/ pi/2-x -tanx)=0

tanx approx 1/ pi/2-x

pi/2

1/(pi/2-x)

x=1.57