What is the limit as x approaches 0 of ((2+x)^2-4)/x ?

The limit as x approaches 0 of ((2+x)^2-4)/x is 4

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limit as x approaches 0 of ((2+x)^2-4)/x

x \to 0 lim (\frac{( 2 + x ) ^{2} - 4}{x})

4

Solution steps

x \to 0 lim (\frac{( 2 + x ) ^{2} - 4}{x})

Simplify

\frac{( 2 + x ) ^{2} - 4}{x} : x + 4

= x \to 0 lim (x + 4)

Plug in the value

x = 0

= 0 + 4

Simplify

= 4

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What is the limit as x approaches 0 of ((2+x)^2-4)/x ?
The limit as x approaches 0 of ((2+x)^2-4)/x is 4