How do I do this limit ?
I need help, not answers or you doing my work. PLEASE JUST HELP....

Question

idku · Answer

$$\Huge \lim_{x~~ \rightarrow~~ \frac{π}{4}}~~~~\frac{\sin(x+\frac{1}{4}π)-1}{x-\frac{1}{4}π }$$

idku · Answer

yes, this is correct limit.

anonymous · Answer

let x =pi/4 +h
so as x--> pi/4 ,
h tends to 0

idku · Answer

pi/4+h ? which  h ?

idku · Answer

if I plug in now, it will be undefined though.

anonymous · Answer

so 
we have 
Lim (h-->0)     (sin(pi/4+h +pi/4) -1)/h

Lim (h-->0)     (sin(pi/2+h) -1)/h

anonymous · Answer

Lim (h-->0) (cosh -1)/h

anonymous · Answer

now we know 1-cosh = (sin (h/2))^2

anonymous · Answer

so can u do further.. now..

anonymous · Answer

1-cosh = (2sin (h/2))^2

Lim (h-->0)    (2*(sin (h/2))^2)/h
Lim (h-->0)    (sin (h/2)/h/2  * sin(h/2)
Lim (h/2-->0)    (sin (h/2)/h/2  * Lim (h-->0)   sin(h/2)  =1*0 =0