Continuity Question
Let :

$\large{ f(x) = \left\{\begin{matrix}
(1+|\sin x|)^{a/|\sin x|} , & -\pi/6

Question

Continuity Question
Let : 

$\large{ f(x) =  \left\{\begin{matrix}
 (1+|\sin x|)^{a/|\sin x|} , &  -\pi/6 < x < 0  \ 
b, & 0\
e^{\tan 2x / \tan 3x } , & 0 < x < \pi / 6 
\end{matrix}\right. }$ 

Determine a and b such that f is continuous at x = 0.

mathslover · Answer

@ganeshie8

mathslover · Answer

@Miracrown

nipunmalhotra93 · Answer

Lim x->0 $$Lim _{x->0}(1+|Sinx|)^{1/|Sinx|}=e$$(1+|sinx|)^(1/|sinx|)

nipunmalhotra93 · Answer

^this will help.. ignore what's written at the end

anonymous · Answer

a = 2/3
b = e^(2/3)

I cheated, don't ask me how XD

mathslover · Answer

Wait, I will be back.... have to go for breakfast...
Sorry :(

anonymous · Answer

Quick question, you just started calc and they gave you this? Or do you like to just make it difficult for us XD

nipunmalhotra93 · Answer

@mathslover use sint/t->1 as t->0 to determine the limit of e^(tan2x/tan3x) as x->0

mathslover · Answer

;p; @iambatman I had completed Differentiation and Application of Derivatives just today... and I have been doing problems on Limits, Continuity and Differentiation...! So, this is one of the problems I was doing

mathslover · Answer

@nipunmalhotra93 I think e is not correct... will it be e^a ?

mathslover · Answer

Oh yes.. you have taken 1 in numerator... and it is a in numerator

so, it will be e^a

nipunmalhotra93 · Answer

yeah

mathslover · Answer

But, I didn't get the 2nd part...

mathslover · Answer

Okay, I got it.

mathslover · Answer

$e^{\cfrac{\tan 2x}{2x} \times \cfrac{3x}{\tan 3x} \times \cfrac{2}{3} }$ 

= $e^{\cfrac{2}{3}}$ = b
and a = 2/3........

mathslover · Answer

Thank you @nipunmalhotra93

nipunmalhotra93 · Answer

np :)