lim-x-4-asin-x-4-cos-pix-1-x-4-x-2-x-3-4-Find-a-

Question Number 35939 by rahul 19 last updated on 26/May/18

\lim_{x \to 4} {(\frac{a \sin (x - 4) + \cos π x - 1}{x - 4})}^{\frac{x - 2}{x - 3}} = 4

F i n d^{'} a^{'} ?

Answered by tanmay.chaudhury50@gmail.com last updated on 26/May/18

t = x - 4

\frac{l i m}{t \to 0} \times {\frac{a s i n t + c o s Π (t + 4) - 1}{t}}^{\frac{t + 2}{t + 1}}

= \frac{l i m}{t \to 0} \times {\frac{a s i n t + c o s Π t - 1}{t}}^{\frac{t + 2}{t + 1}}

= \frac{l i m}{t \to 0} \times {\frac{a s i n t}{t} - \frac{2 {s i n}^{2} (\frac{Π t}{2})}{t}}^{\frac{t + 2}{t + 1}}

= \frac{l i m}{t \to 0} \times {\frac{a s i n t}{t} - 2 \frac{s i n (\frac{Π t}{2})}{(\frac{Π t}{2})} \times \frac{Π}{2} \times s i n \frac{Π t}{2}}^{\frac{t + 2}{t + 1}}

= a^{2}

s o a^{2} = 4 a \pm 2

Commented by rahul 19 last updated on 26/May/18

Is a=-2 acceptable ?

Commented by rahul 19 last updated on 26/May/18

T h a n k Y o u s i r .

Commented by tanmay.chaudhury50@gmail.com last updated on 26/May/18

s o f a r n o p r o b l e m c o n s i d e r i n g a = - 2 i n t h e

q u e s t i o n \dots

Commented by Joel579 last updated on 26/May/18

Sir Tanmay, you can tap the^{'} \sin^{'} button next to

the^{'} {SEL}^{'} button, and then press^{'} \lim_{x \to 0}^{'} button

{It}^{'} s just tips so you {won}^{'} t type limit manually

Commented by tanmay.chaudhury50@gmail.com last updated on 26/May/18

t h a n k y o u s i r . .