What happens to a function `f(x)` at `x=a` , if `(lim)_(x->a)f(x)=f(a)`

For the function f(x) = 2 . Find lim_(x to 1) f(x)

For the function f(x) = 4x . Find lim_(x to 2) f (x)

For the function f(x)=x+1/x Find f ' (x)

If f is continuous at a then [f ,a]=lim x->a f(x)-f(a)

If the function f(x) satisfies (lim)_(x->1)(f(x)-2)/(x^2-1)=pi, evaluate (lim)_(x->1)f(x)

Integrate the functions f(x) f(x)=x log(x)

Left hand derivative and right hand derivative of a function f(x) at a point x=a are defined as f'(a^-)=lim_(hrarr0^(+))(f(a)-f(a-h))/(h) =lim_(hrarr0^(+))(f(a+h)-f(a))/(h) andf'(a^(+))=lim_(hrarr0^(+))(f(a+h)-f(a))/(h) =lim_(hrarr0^(+))(f(a)-f(a+h))/(h) =lim_(hrarr0^(+)) (f(a)-f(x))/(a-x) respectively. Let f be a twice differentiable function. We also know that derivative of a even function is odd function and derivative of an odd function is even function. If f is even function, which of the following is right hand derivative of f' at x=a?

If f(x) is differentiable at x=a , find (lim)_(x->a)(x^2f(a)-a^2\ f(x))/(x-a) .

Given a real-valued function f such that f(x)={(tan^2{x})/((x^2-[x]^2) sqrt({x}cot{x}),for x 0 Where [x] is the integral part and {x} is the fractional part of x , then ("lim")_(xvec0^+)f(x)=1 , ("lim")_(xvec0^-)f(x)=cot1 , cot^(-1)(("lim")_(xvec0^-)f(x))^2=1 , tan^(-1)(("lim")_(xvec0^+)f(x))=pi/4

Let f(x)=(x^2-9x+20)/(x-[x]) (where [x] is the greatest integer not greater than xdot Then (A) ("lim")_(x->5)f(x)=1 (B) ("lim")_(x->5)f(x)=0 (C) ("lim")_(x->5)f(x) does not exist. (D)none of these