Evaluate the Limit

Problem

(lim_h→0)(((3+h)2−9)/h)

Solution

1. Expand the squared binomial in the numerator using the formula (a+b)2=a2+2*a*b+b2

(lim_h→0)((9+6*h+h2−9)/h)

2. Simplify the numerator by subtracting the constants 9 - 9$.

(lim_h→0)((6*h+h2)/h)

3. Factor out the common term h from the numerator.

(lim_h→0)((h*(6+h))/h)

4. Divide the numerator and denominator by h to remove the indeterminate form.

(lim_h→0)(6+h)

5. Evaluate the limit by substituting h=0 into the remaining expression.

6+0=6

Final Answer

(lim_h→0)(((3+h)2−9)/h)=6

Want more problems? Check here!