If `f` is an even function, then prove that `lim_(x->0^-) f(x) = lim_(x->0^+) f(x)`

If f is an even function , then prove that Lim_( xto 0^(-)) f(x) = Lim_(x to 0^(+)) f(x) , whenever they exist .

If f is an even function,then prove that lim_(x rarr0^(-))f(x)=lim_(x rarr0^(+))f(x)

If ‘f' is an even function, prove that lim_(x rarr 0^-) f(x)= lim_(x rarr 0^+) f(x) .

If f is an even function, prove that lim_(xto0^(-)) (x)=lim_(xto0^(+)) f(x).

Prove that lim_(x->0) (f(x+h)+f(x-h)-2f(x))/h^2 = f''(x)

If |f(x)|lex^(2), then prove that lim_(xto0) (f(x))/(x)=0.

If |f(x)|lex^(2), then prove that lim_(xto0) (f(x))/(x)=0.

If |f(x)|lex^(2), then prove that lim_(xto0) (f(x))/(x)=0.

If |f(x)|lex^(2), then prove that lim_(xto0) (f(x))/(x)=0.

If f(x) is an odd function and lim_(x rarr 0) f(x) exists, then lim_(x rarr 0) f(x) is