Cool limit

Calculus Level 3

lim ⁡ x → π / 2 1 − sin ⁡ x ( π 2 − x ) 2 = ? \large \lim_{x\to \pi/2} \dfrac{ 1- \sin x}{\left( \frac\pi2 - x \right)^2 } = \, ?


The answer is 0.5.

Shivamani Patil by shivamani patil , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Punith N.S.
May 1, 2014

This limit gives us a indeterminate form of 0/0 when you plug in the value of x.Hence,we can use L'Hopitals Rule. We find the first derivative which turns out to be the limit as x tends to pi/2 ( -cos x)/(2x-pi).But this is again in the indeterminate form of 0/0.Hence,Differentiating again we get limit x tends to pi/2 sin x/2.Now plugging in the value of x we get the answer is 1/2

1 Helpful 0 Interesting 0 Brilliant 0 Confused

good

shivamani patil - 7 years, 1 month ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...