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 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

Examine whether the function f given by f(x)= x^2 is continuous at x= 0.

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

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

If the function f is defined by f(x)={(x+2," if" xgt1), (2" if" -1lexle1 ), (x-1 " if" -3ltxlt-1):} find the values of f(0)

if the function f(x)=AX-B X =2 is continuous at x=1 and discontinuous at x=2 find the value of A and B

Show that the function f given by f(x)= {{:(x^3+3," if "x ne 0),(1," if "x=0):} is not continuous at x=0.

The probability density function of X is given by f(x)={{:(kxe^(-2x), "for " x gt 0), (0, "for " x le 0):} Find the value of k.

If f'(x)=f(x)+int_(0)^(1)f(x)dx ,given f(0)=1 , then the value of f(log_(e)2) is