Continuity and Differentiability
Examine the continuity of the function f(x)=2x2−1at x=3.
be a continuous function such that f(x+y)=f(x)+f(y)+f(x)f(y),∀x∈R˙
If f is an even function such that (lim)h0hf(h)−f(0) has some finite non-zero value, then prove that f(x) is not differentiable at x=0.
A curve in the xy-plane is parametrically given by x=t+t3andy=t2,wheret∈R is the parameter. For what value(s) of t is dxdy=21? 31 b. 2 c. 3 d. 1