# Determine the limit of each function analytically. Show neat and complete soluti

Determine the limit of each function analytically. Show neat and complete solution. (hint: some of the items need to be factored or rationalized for the limits to exist)
$\underset{h\to 0}{lim}\frac{{\left(1+h\right)}^{2}-{1}^{2}}{h}$
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Ezra Herbert
Given:
Find the limit of: $\underset{h\to 0}{lim}\frac{{\left(1+h\right)}^{2}-{1}^{2}}{h}$
Solution:
$\underset{h\to 0}{lim}\frac{{\left(1+h\right)}^{2}-{1}^{2}}{h}=\underset{h\to 0}{lim}\frac{\left(1+h+1\right)\left(1+h-1\right)}{h}$
$\left[\therefore \left({a}^{2}-{b}^{2}\right)-\left(a+b\right)\left(a-b\right)\right]$
$=\underset{h\to 0}{lim}\frac{\left(h+2\right)\left(h\right)}{h}$
$=\underset{h\to 0}{lim}\left(h+2\right)$
$=0+2$
$\underset{h\to 0}{lim}\frac{{\left(1+h\right)}^{2}-{1}^{2}}{h}=2$
Jeffrey Jordon