What is the limit as x approaches+0 of ((1+x)^4-1)/x ?

The limit as x approaches+0 of ((1+x)^4-1)/x is 4

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limit as x approaches+0 of ((1+x)^4-1)/x

x \to + 0 lim (\frac{( 1 + x ) ^{4} - 1}{x})

4

Solution steps

x \to 0 lim (\frac{( 1 + x ) ^{4} - 1}{x})

Simplify

\frac{( 1 + x ) ^{4} - 1}{x} : (x^{2} + 2 x + 2) (x + 2)

= x \to 0 lim ((x^{2} + 2 x + 2) (x + 2))

Plug in the value

x = 0

= (0^{2} + 2 \cdot 0 + 2) (0 + 2)

Simplify

(0^{2} + 2 \cdot 0 + 2) (0 + 2) : 4

= 4

What is the limit as x approaches+0 of ((1+x)^4-1)/x ?
The limit as x approaches+0 of ((1+x)^4-1)/x is 4