What is the limit as x approaches infinity of (ln(x)+x)/(xnx) ?

The limit as x approaches infinity of (ln(x)+x)/(xnx) is 0

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limit as x approaches infinity of (ln(x)+x)/(xnx)

x \to \infty lim (\frac{ln ( x ) + x}{x n x})

0

Solution steps

x \to \infty lim (\frac{ln ( x ) + x}{x n x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{n} \cdot x \to \infty lim (\frac{ln ( x ) + x}{xx})

Expand

\frac{ln ( x ) + x}{xx} : \frac{ln ( x )}{x ^{2}} + \frac{1}{x}

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

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

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

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

= \frac{1}{n} (0 + 0)

Simplify

= 0

f (x) = \frac{3 x ^{2} + 1}{x ^{\frac{3}{2}}}

\int e^{i 8 x} cos (4 x) d x

f (x) = \frac{x ^{2} - 5 x}{x + 1}

\int 3 x^{2} x^{3} - 5 d x

\frac{d}{d x} (\frac{- x}{x ^{2} + y ^{2}})

What is the limit as x approaches infinity of (ln(x)+x)/(xnx) ?
The limit as x approaches infinity of (ln(x)+x)/(xnx) is 0