# Evaluate limit as x approaches 2 of (f(x)-f(x))/(x-2)

Take the limit of each term.
Subtract from .
Apply L’Hospital’s rule.
Evaluate the limit of the numerator and the limit of the denominator.
Take the limit of the numerator and the limit of the denominator.
Evaluate the limit of which is constant as approaches .
Evaluate the limit of the denominator.
Split the limit using the Sum of Limits Rule on the limit as approaches .
Evaluate the limits by plugging in for all occurrences of .
Evaluate the limit of by plugging in for .
Evaluate the limit of which is constant as approaches .
Subtract from .
The expression contains a division by The expression is undefined.
Undefined
The expression contains a division by The expression is undefined.
Undefined
Since is of indeterminate form, apply L’Hospital’s Rule. L’Hospital’s Rule states that the limit of a quotient of functions is equal to the limit of the quotient of their derivatives.
Find the derivative of the numerator and denominator.
Differentiate the numerator and denominator.
Since is constant with respect to , the derivative of with respect to is .
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .