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???
(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?