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

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

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

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

0

Solution steps

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

Divide by

e^{x} : \frac{\frac{x}{e ^{x}}}{\frac{6}{e ^{x}} + 1}

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

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

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

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

= \frac{0}{1}

Apply rule

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

= 0

\int (\frac{4 - t + t ^{2}}{t ^{2}}) d t

\frac{d}{d x} (ln (x^{2} + 20))

\frac{\partial}{\partial x} (\frac{2 y}{x ^{2} + 1})

x \to 3 lim (\frac{x - 2}{x + 2})

x \to 1800 lim (28 π^{2})

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