If the function `f(x)=((128 a+a x)^(1/8)-2)/((32+b x)^(1/5)-2)` is continuous at `x=0` , then the value of `a/b` is (A) `3/5f(0)` (B) `2^(8/5)f(0)` (C) `(64)/5f(0)` (D) none of these

If the function f: Rsetminus {0}vec given by f(x)=1/x-2/(e^(2x)-1) is continuous at x=0, then find the value of f(0)

If f(x)={(1-cos(1-cos x/2))/(2^m x^n)1x=0,x!=0 and f(0)=1 is continuous at x=0 then the value of m+n is a. 2 b. 3 c. -3 d. 7

If f(x) = int(5x^(8)+7x^(6))/((x^(2)+1+2x^(7))^(2))dx, (x ge 0) , and f(0) = 0, then the value of f(1) is

If f(x)={(sin(2x^2)/a+cos((3x)/b))^a b//x^2,x!=0e^3, x=0 is continuous at x=0AAb in R then minimum value of a is -1//8 b. -1//4 c. -1//2 d. 0

If f^(prime)(x)=f(x)+int_0^1f(x)dx ,gi v e nf(0)=1, then the value of f((log)_2 2) is (a) 1/(3+e) (b) (5-e)/(3-e) (c) (2+e)/(e-2) (d) none of these

The function f(x)=sin^(-1)(cosx) is (a) discontinuous at x=0 (b) continuous at x=0 (c) differentiable at x=0 (d) none of these

Prove that the function f(x)= 5x-3 is continuous at x=0, at x= -3" and at " x=5 .

If the function f(x)=a x^3+b x^2+11 x-6 satisfies conditions of Rolles theorem in [1,3] and f'(2+1/(sqrt(3)))=0, then values of a and b , respectively, are (A) -3,2 (B) 2,-4 (C) 1,-6 (D) none of these

Let f be a continuous, differentiable, and bijective function. If the tangent to y=f(x)a tx=a is also the normal to y=f(x)a tx=b , then there exists at least one c in (a , b) such that (a) f^(prime)(c)=0 (b) f^(prime)(c)>0 (c) f^(prime)(c) (d) none of these

A continuous real function f satisfies f(2x)=3(f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx