Science:Math Exam Resources/Courses/MATH110/December 2013/Question 10 (a)/Solution 1

A function $f(x)$ is differentiable at the point $x=2$ if the following limit exists

$\lim _{x\to 2}{\frac {f(x)-f(2)}{x-2}}$

Equivalently, $f(x)$ is differentiable at the point $x=2$ if the following limit exists

$\lim _{h\to 0}{\frac {f(2+h)-f(2)}{h}}$