Question

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

Answer 1

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

Answer 2

yes, this is correct limit.

Answer 3

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

Answer 4

pi/4+h ? which h ?

Answer 5

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

Answer 6

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

Lim (h-->0) (sin(pi/2+h) -1)/h

Answer 7

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

Answer 8

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

Answer 9

so can u do further.. now..

Answer 10

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