a.) Let f(x)=(sin x)/x, x≠0. Define f(0) such that f is continuous at x=0.
b.) Prove that if x0 is critical point of function f (f(0) defined as in part a), then |f(x0)|=1/(1+x02)-½ (Hint: use the basic properties of sine and cosine with given information.)
The Attempt at a Solution
a.)Easy. Let f(0)=1, because (sin x)/x approaches 1 when x--->0 so f(0) has to be equal to 1.
b.) I have no idea how to begin :/