# Limit value using definition of derivative

1. Nov 1, 2011

### karkas

1. The problem statement, all variables and given/known data
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???

2. Relevant 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)

3. The attempt at a solution
That would mean that (a) = f ' (1) = pi/4 * (√2)/2 , right?

2. Nov 1, 2011

### lurflurf

yes that is right

3. Nov 1, 2011

### karkas

Ok, excellent, thanks!