Let `f(x)=1/(1+e^(1/x))for\ x!=0\ a n d\ f(0)=0` , then `f(0^+)` does not exist b. `f(0)` is equal to zero c. `f^(prime)(0^-)\ ` is equal to 1 d. `f^(prime)(0^+)` is equal to zero

Let f be defined on R by f(x)= x^(4)sin(1/x) , if x!=0 and f(0)=0 then (a) f'(0) doesn't exist (b) f'(2-) doesn't exist (c) f'' is not continous at x=0 (d) f''(0) exist but f'' is not continuous at x=0

Let f be defined on R by f(x)=x^(4)sin(1/x) , if x!=0 and f(0)=0 then (a) f'(0) doesn't exist (b) f'(2-) doesn't exist (c) f'' is not continous at x=0 (d) f''(0) exist but f''' is not continuous at x=0

Let f be differentiable function such that f'(x)=7-3/4(f(x))/x,(xgt0) and f(1)ne4" Then " lim_(xto0^+) xf(1/x) is (A) exists and equals to 4 (B) does not exist (C) exists and equals to 0 (D) exists and equals 4//7 .

If f(x) = (x^n-a^n)/(x-a) , then f'(a) is a. 1 b. 1/2 c. 0 d. does not exist

If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

If [.] is the greatest integer function and f(x)=[tan^2x], then (a) ("lim")_(xvec0)f(x) does not exist (b) f(x) is continuous at x=0 (c) f(x) is not differentiable at x=0 (d) f^(prime)(0)=1

If [.] is the greatest integer function and f(x)=[tan^2x], then (a) ("lim")_(xvec0)f(x) does not exist (b) f(x) is continuous at x=0 (c) f(x) is not differentiable at x=0 (d) f^(prime)(0)=1

Let f((x+y)/(2))=1/2 |f(x) +f(y)| for all real x and y, if f '(0) exists and equal to (-1), and f(0)=1 then f(2) is equal to-

If f(x)=int_0^1(dt)/(1+|x-t|) ,then f^(prime)(1/2) is equal to (a)0 (b) 1/2 (c) 1 (d) none of these