Let `f(x)=(lim)_(n rarr oo)sum_(r=0)^(n-1)x/((r x+1){(r+1)x+1})` . Then (A) `f(x)` is continuous but not differentiable at `x=0` (B) `f(x)` is both continuous but not differentiable at `x=0` (C) `f(x)` is neither continuous not differentiable at `x=0` (D) `f(x)` is a periodic function.

Show that the function f(x)=x|x| is continuous and differentiable at x = 0

Let f:[a,b]rarr[1,infty) be a continuous function and lt g: RrarrR be defined as g(x)={(0, "if x" lt a),(int_a^x f(t)dt, "if a"lexleb),(int_a^b f(t)dt, "if x"gtb):} Then a) g(x) is continuous but not differentiable at a b) g(x) is differentiable on R c) g(x) is continuous but nut differentiable at b d) g(x) is continuous and differentiable at either a or b but not both.

The function f (x) is continuous at x = 0 of -

Prove that the function f given by f(x)= |x-1|, x in R is not differentiable at x= 1.

If f(x)={x ,xlt=1,x^2+b x+c ,x >1 find b and c if function is continuous and differentiable at x=1

Examine the continuity and differentiability of the function f(x)=|sinx|atx=0 .

Let f(x)={(-,1, -2lexlt0),(x^2,-1,0lexlt2):} if g(x)=|f(x)|+f(|x|) then g(x) in (-2,2) is (A) not continuous is (B) not differential at one point (C) differential at all points (D) not differential at two points

If f(x)= {|x|-|x-1|}^2 , draw the graph of f(x) and discuss its continuity and differentiability of f(x)

f(x)=(lim)_(n->oo)(sin(pix/2))^(2n) for x >0,x!=1 ,and f(1)=0. Discuss the continuity at x=1.

Let f:Rto R be a twice continuously differentiable function such that f(0)=f(1)=f'(0)=0 . Then