A function `f(x)` is defined as follows : `f(x) ={x^2, if x != 1 and 1 ,if x=1` Prove that `lim_(x->1) f(x)=1`.

A function f(x) is defined as follows: f(x)=1 if x>0;-1 if x<0;0 if x=0. Prove that lim_(x rarr0)f(x) does not exist

The function f(x), for which f(x)={x^(2),xne1 2, x=1} Show that: lim_(x to 1) f(x)=1

The function f(x), for which f(x)={x^(2),xne1 2, x=1} Show that: lim_(x to 1) f(x)=1

If f(x) is defined as f(x)={{:(x,0le,xle1),(1,x,=1),(2-x,x,gt1):} then show that lim_(Xrarr1) f(x)=1

If f(x) is defined as f(x)={{:(x,0le,xle1),(2,x,=1),(20x,x,gt1):} then show that lim_(Xrarr1) f(x)=1

A function f (x) is defined as follwos : f(x){:(=2x+1," when "xle 1),(= 3-x," when "xgt1):} Examine whether underset(xrarr1)"lim"f(x) exists or not.

A function f defined by f(x)=In(sqrt(x^(2)+1-x)) is

Consider the function : f (x) ={(x+2, x ne 1),(0,x=1):} . To find lim_(x to 1) f(x) .

If fthe function f(x) satisfies lim_(x rarr 1) (f(x) - 2)/(x^2 - 1) = pi , evaluate lim_(x rarr 1) f(x).

If the function f:[1,∞)→[1,∞) is defined by f(x)=2 ^(x(x-1)) then f^-1(x) is