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

Suppose f(x) and g(x) are two continuous function defined for 0 le xle 1 . Given , f(x)= int_(0)^(1) e^(x+1) . F(t) dt and g(x)=int _(0)^(1) e^(x+t). G(t) dt +x , The value of f(1) equals

Let f(x) and g(x) be two continuous functions defined from R rarr R, such that f(x_(1))>f(x_(2)) and g(x_(1)) f(g(3 alpha-4))

If f(x) and g(x) are two continuous functions defined on [-a,a], then the value of int_(-a)^(a){f(x)+f(-x)}{g(x)-g(-x)}dx is

If f(x) and g(x) are two continuous functions defined on [-a,a] then the the value of int_(-a)^(a) {f(x)f+(-x) } {g(x)-g(-x)}dx is,

Let f(x)=[x], where [.] is the greatest integer fraction and g(x)=sin x be two valued functions over R. Which of the following statements is correct? (a) Both f(x) and g(x) are continuous at x=0 (b) f(x) is continuous at x=0, but g(x) is not continuous at x=0. (c) g(x) is continuous at x=0, but f(x) is not continuous at x=0. (d) Both f(x) and g(x) are discontinuous at x=0

Prove that the function defined by f(x)= tan x is a continuous function.

Show that the function defined by f(x)= sin (x^(2)) is a continuous function