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

1.	If f is an even function, prove that `lim_(xto0^(-)) (x)=lim_(xto0^(+)) f(x).`
Answer» Let f be an even function Then, `underset(xto0^(-))limf(x)=underset(hto0)limf(0-h)=underset(hto0)limf(-h)` `=underset(hto0)limf(h)" "[becausef"being even,"f(-h=f(h)]=underset(hto0)limf(0+h)=underset(xto0^(+))limf(x).` Hence, `underset(xto0^(-))limf(x)=underset(xto0^(+))limf(x).`

Discussion