Limit value using definition of derivative

[karkas]

Homework Statement

I have encountered a limit that I wasn't really sure whether I was solving right, it's limit (a). I thought that I could find it considering a function f(x) (b) , find the derivative of that function and substitute x->1 so that I can find the value of the limit. Is this correct thinking?

Homework Equations

(a) lim(x->1) [ sin(x*pi/4) - sin(pi/4) ] / x-1

(b) f(x) = sin(x *pi/4) and so f ' (x) = pi/4 cos(x* pi/4)

The Attempt at a Solution

That would mean that (a) = f ' (1) = pi/4 * (√2)/2 , right?

 

[lurflurf]

yes that is right

 

[karkas]

Ok, excellent, thanks!