What is the limit as x approaches infinity of (e^x)/(ln(x)+2) ?

The limit as x approaches infinity of (e^x)/(ln(x)+2) is infinity

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limit as x approaches infinity of (e^x)/(ln(x)+2)

x \to \infty lim (\frac{e ^{x}}{ln ( x ) + 2})

\infty

Solution steps

x \to \infty lim (\frac{e ^{x}}{ln ( x ) + 2})

Divide by

ln (x) : \frac{\frac{e ^{x}}{l n ( x )}}{1 + \frac{2}{l n ( x )}}

= x \to \infty lim (\frac{\frac{e ^{x}}{l n ( x )}}{1 + \frac{2}{l n ( 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} ( \frac{e ^{x}}{l n ( x )} )}{lim _{x \to \infty} ( 1 + \frac{2}{l n ( x )} )}

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

x \to \infty lim (1 + \frac{2}{ln ( x )}) = 1

= \frac{\infty}{1}

Apply Infinity Property:

\frac{\infty}{c} = \infty

= \infty

x \to 0 lim (\frac{- x - ln ( 1 - x )}{8 x ^{2}})

x \to 1 lim (\frac{x + 1}{2 x - 1})

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

x \to 0 lim (\frac{csc ^{2} ( x )}{cot ^{2} ( x )})

x \to \infty lim (\frac{6 x ^{2} - 7 x + 10}{5 x ^{3} + 2 x ^{2} - 4 x + 5})

What is the limit as x approaches infinity of (e^x)/(ln(x)+2) ?
The limit as x approaches infinity of (e^x)/(ln(x)+2) is infinity