[(2+h)^2-4]/h
find the limit
how do i do this?
To find the limit of the expression [(2+h)^2-4]/h as h approaches a certain value, you can follow these steps:
1. Substitute the value that h approaches into the expression. In this case, let's assume h approaches 0. So substitute 0 for h in the given expression: [(2+0)^2-4]/0.
2. Simplify the expression. Since we substituted 0 for h, the expression becomes [(2+0)^2-4]/0 = [2^2-4]/0 = [4-4]/0 = 0/0.
3. Notice that the expression has now become an indeterminate form of 0/0. This means we cannot directly evaluate the limit using substitution.
4. To evaluate the limit in this case, we can use algebraic manipulation. Expand out the numerator using the binomial square formula: [(2+h)^2-4] = (4 + 4h + h^2 - 4) = (h^2 + 4h).
5. Now we have (h^2 + 4h)/h = (h(h + 4))/h = (h + 4). Notice that the simplified expression no longer contains h in the denominator.
6. Finally, taking the limit as h approaches 0, we substitute 0 into the simplified expression: lim (h + 4) as h approaches 0. The result is 0 + 4 = 4.
Therefore, the limit of the expression [(2+h)^2-4]/h as h approaches 0 is 4.