What is the limit as x approaches infinity of (arctan(x))/(1/x-4) ?

The limit as x approaches infinity of (arctan(x))/(1/x-4) is -pi/8

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limit as x approaches infinity of (arctan(x))/(1/x-4)

x \to \infty lim (\frac{arctan ( x )}{\frac{1}{x} - 4})

- \frac{π}{8}

Decimal Notation

- 0.39269 \dots

Solution steps

x \to \infty lim (\frac{arctan ( x )}{\frac{1}{x} - 4})

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} ( arctan ( x ) )}{lim _{x \to \infty} ( \frac{1}{x} - 4 )}

x \to \infty lim (arctan (x)) = \frac{π}{2}

x \to \infty lim (\frac{1}{x} - 4) = - 4

= \frac{\frac{π}{2}}{- 4}

Simplify

\frac{\frac{π}{2}}{- 4} : - \frac{π}{8}

= - \frac{π}{8}

\frac{d}{d x} (- \frac{x ^{7}}{7} + \frac{x ^{5}}{5})

y = \frac{3 x - 2}{2 x + 1}

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

\int \frac{x ^{3}}{( x ^{2} + a ^{2} ) ^{3}} d x

y = 3 x, x + y = 4, y = 1

What is the limit as x approaches infinity of (arctan(x))/(1/x-4) ?
The limit as x approaches infinity of (arctan(x))/(1/x-4) is -pi/8