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Popular >

limit as x approaches infinity of 1/(sqrt(x^2+17x)-\sqrt{x^2+5x)}

Solution

x \to \infty lim (\frac{1}{x ^{2} + 17 x - x ^{2} + 5 x})

Solution

\frac{1}{6}

+1

Decimal

0.16666 \dots

Solution steps

x \to \infty lim (\frac{1}{x ^{2} + 17 x - x ^{2} + 5 x})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( x ^{2} + 17 x - x ^{2} + 5 x )}

x \to \infty lim (1) = 1

x \to \infty lim (x^{2} + 17 x - x^{2} + 5 x) = 6

= \frac{1}{6}

Graph

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Frequently Asked Questions (FAQ)

What is the limit as x approaches infinity of 1/(sqrt(x^2+17x)-\sqrt{x^2+5x)} ?
The limit as x approaches infinity of 1/(sqrt(x^2+17x)-\sqrt{x^2+5x)} is 1/6