Q. 64 - Calculus

Question

Calculate each of the limits:

$\underset{h\to 0}{\lim }\frac{{(2+h)}^2-2^2}{h}$.

Step-by-Step Solution

Answer

The solution of the limit $\underset{h\to 0}{\lim }\frac{{(2+h)}^2-2^2}{h}$ is, $4$.

Step 1. Given Information.

The limit is,

$\underset{h\to 0}{\lim }\frac{{(2+h)}^2-2^2}{h}$.

Step 2. Finding the solution.

$\underset{h\to 0}{\lim }\frac{{(2+h)}^2-2^2}{h}$

Using ${(a+b)}^2=a^2+2ab+b^2$,

$$\begin{gathered} =\underset{h\to 0}{\lim }\frac{h^2+4h+4-4}{h} \\ =\underset{h\to 0}{\lim }\frac{h^2+4h}{h} \\ =\underset{h\to 0}{\lim }h+4 \end{gathered}$$

Inputting $h=0$

$$\begin{gathered} =0+4 \\ =4 \end{gathered}$$