Consider two functions `f(x)` and `g(x)` which are continuous and defined for `0<=x<=1` .Given `f(x)=int_(0)^(1)e^(x+t)*f(t)dt` and `g(x)=x+int_(0)^(1)e^(x+t)*g(t)dt`.The Value of `g(0)-f(0)`

If f(x) be continuous function and g(x) be discontinuous, then

Suppose f(x) and g(x) are two continuous functions defined for 0<=x<=1. Given,f(x)=int_(0)^(1)e^(x+1)*f(t)dt and g(x)=int_(0)^(1)e^(x+1)*g(t)dt+x The value of f(1) equals

Consider two functions,f(x) and g(x) defined as under: f(x)={1+x^(3),x =0 and g(x)={(x-1)^((1)/(3))(x+1)^((1)/(2)),x =0 Evaluate g(f(x))

Consider the function f (x) and g (x), both defined from R to R f (x) = (x ^(3))/(2 )+1 -x int _(0)^(x) g (t) dt and g (x) =x - int _(0) ^(1) f (t) dt, then The number of points of intersection of f (x) and g (x) is/are:

In order that the function f(x) = (x+1)^(cot x) is continuous at x=0 , the value of f(0) must be defined as :

Consider the function f(x)=x^(30)ln x^(20) for x>0 If f is continuous at x=0 then f(0) is equal to 0( b) is equal to (2)/(3) is equal to 1 can not be defined to make f(x) continuous at x=0

Let function f be defined as f:R^(+)toR^(+) and function g is defined as g:R^(+)toR^(+) . Functions f and g are continuous in their domain. Suppose, the function h(x)=lim_(ntooo)(x^(n)f(x)+x^(2))/(x^(n)+g(x)), x gt0 . If h(x) is continuous in its domain,then f(1).g(1) is equal to

In order that the function f(x) = (x+1)^(1/x) is continuous at x = 0, f(0) must be defined as