What is the limit as x approaches 0 of ((1+x)^3-1)/x ?

The limit as x approaches 0 of ((1+x)^3-1)/x is 3

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limit as x approaches 0 of ((1+x)^3-1)/x

x \to 0 lim (\frac{( 1 + x ) ^{3} - 1}{x})

3

Solution steps

x \to 0 lim (\frac{( 1 + x ) ^{3} - 1}{x})

Simplify

\frac{( 1 + x ) ^{3} - 1}{x} : x^{2} + 3 x + 3

= x \to 0 lim (x^{2} + 3 x + 3)

Plug in the value

x = 0

= 0^{2} + 3 \cdot 0 + 3

Simplify

= 3

\frac{d}{d x} (sin (\frac{π}{x}))

x \to 0 lim (\frac{1}{sin ( x ^{2} )})

\int \frac{5}{x ( x ^{4} + 1 )} d x

\int \frac{2 x ^{2} + 16}{x ( x - 2 ) ^{3}} d x

\frac{d}{d x} (\frac{x ^{3}}{1 - x ^{2}})

What is the limit as x approaches 0 of ((1+x)^3-1)/x ?
The limit as x approaches 0 of ((1+x)^3-1)/x is 3