What is the limit as x approaches infinity of sin(arctan(x)) ?

The limit as x approaches infinity of sin(arctan(x)) is 1

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limit as x approaches infinity of sin(arctan(x))

x \to \infty lim (sin (arctan (x)))

1

Solution steps

x \to \infty lim (sin (arctan (x)))

Simplify

sin (arctan (x)) : \frac{x}{1 + x ^{2}}

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

Divide by highest denominator power:

\frac{1}{\frac{1}{x ^{2}} + 1}

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

x \to \infty lim (1) = 1

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

= \frac{1}{1}

Simplify

= 1

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

\frac{\partial}{\partial x} (4 x (5 + y)^{- 1})

y^{^{'}} + 2 x y = x^{3}

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

\frac{d}{d x} (x (x^{2} - 4))

What is the limit as x approaches infinity of sin(arctan(x)) ?
The limit as x approaches infinity of sin(arctan(x)) is 1