Evaluate the Limit

Problem

(lim_x→4)((x2−16)/(x−4))

Solution

1. Identify the indeterminate form by substituting x=4 into the expression, which results in (4−16)/(4−4)=0/0

2. Factor the numerator using the difference of squares formula, a2−b2=(a−b)*(a+b)

x2−16=(x−4)*(x+4)

3. Simplify the expression by canceling the common factor (x−4) from the numerator and the denominator, noting that x≠4 as it approaches the limit.

((x−4)*(x+4))/(x−4)=x+4

4. Evaluate the limit by substituting x=4 into the simplified expression.

4+4=8

Final Answer

(lim_x→4)((x2−16)/(x−4))=8

Want more problems? Check here!