If for a function `f(x),f'(a)=0,f"(a)=0,f'''(a)gt0,` then at `x=a,f(x)` is

The function f(x)= xcos(1/x^2) for x != 0, f(0) =1 then at x = 0, f(x) is

There exists a function f(x) satisfying f(0)=1, f'(0)=-1, f(x) gt 0 , for all x, then :

Let f be a function such that f"'(x) is continuous, f(x) ge 0, f(0) = 0,f'(0)=0, and f"(0) gt 0 The graph of f is shown below. Find the limit as x->0^+of the quotient (Area under curve and above [0,x])/( Area of triangle OAP)

Let f(x) be a function such that,f(0)=f'(0)=0,f''(x)=sec^(4)x+4 then the function is

If f(x)=a^(x), a gt 0 , then f is

If f(x) is a continuous function satisfying f(x)f(1/x) =f(x)+f(1/x) and f(1) gt 0 then lim_(x to 1) f(x) is equal to