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Popular Calculus >

limit as x approaches infinity of (sqrt(1+\sqrt{x)})/(\sqrt[3]{1+x)}

Solution

x \to \infty lim (\frac{1 + x}{3 1 + x})

Solution

Does not exist

Solution steps

x \to \infty lim (\frac{1 + x}{3 1 + x})

Multiply by the conjugate of

1 + x : \frac{1 - x}{1 - x}

= x \to \infty lim \frac{\frac{1 - x}{1 - x}}{3 1 + x}

Simplify

\frac{\frac{1 - x}{1 - x}}{3 1 + x} : \frac{1 - x}{1 - x 3 1 + x}

= x \to \infty lim (\frac{1 - x}{1 - x 3 1 + x})

\frac{1 - x}{1 - x 3 1 + x}

undefined for

x

approaching

\infty

= Does not exist

Graph

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x \to \infty lim (- 8 (\frac{3}{x}))

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Frequently Asked Questions (FAQ)

What is the limit as x approaches infinity of (sqrt(1+\sqrt{x)})/(\sqrt[3]{1+x)} ?
The limit as x approaches infinity of (sqrt(1+\sqrt{x)})/(\sqrt[3]{1+x)} is Does not exist