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

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

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

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

4

Solution steps

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

Simplify

\frac{( x + 1 ) ^{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

\int x sin (x^{2} + 4) d x

x \frac{d y}{d x} - 2 y = 6 x^{5}

y^{^{''}} + 6 y^{^{'}} + 9 y = 18 t^{2} + 24 t + 4

f (x) = \frac{1}{x + 5}

\int_{0}^{\frac{π}{2}} 5 cos^{2} (x) d x

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