What is the limit as x approaches infinity of x/(sqrt(x^3+6)) ?

The limit as x approaches infinity of x/(sqrt(x^3+6)) is 0

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limit as x approaches infinity of x/(sqrt(x^3+6))

x \to \infty lim (\frac{x}{x ^{3} + 6})

0

Solution steps

x \to \infty lim (\frac{x}{x ^{3} + 6})

Divide by

x^{\frac{3}{2}} : \frac{\frac{1}{x ^{\frac{1}{2}}}}{1 + \frac{6}{x ^{3}}}

= x \to \infty lim \frac{\frac{1}{x ^{\frac{1}{2}}}}{1 + \frac{6}{x ^{3}}}

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} ( \frac{1}{x ^{\frac{1}{2}}} )}{lim _{x \to \infty} ( 1 + \frac{6}{x ^{3}} )}

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

x \to \infty lim (1 + \frac{6}{x ^{3}}) = 1

= \frac{0}{1}

Apply rule

\frac{0}{a} = 0, a \neq = 0

= 0

\frac{\partial}{\partial x} (ln (x + z))

\int 5 sin (6 x) + 6 sin (5 x) d x

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

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

y = (2 x + 1)^{3} + 6 x (2 x + 1)^{2}

What is the limit as x approaches infinity of x/(sqrt(x^3+6)) ?
The limit as x approaches infinity of x/(sqrt(x^3+6)) is 0