What is the limit as x approaches infinity of ((sin^2(x)))/(x+e^{-x)} ?

The limit as x approaches infinity of ((sin^2(x)))/(x+e^{-x)} is 0

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limit as x approaches infinity of ((sin^2(x)))/(x+e^{-x)}

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

0

Solution steps

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

Divide by highest denominator power:

\frac{\frac{s i n ^{2} ( x )}{x}}{1 + \frac{e ^{- x}}{x}}

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

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

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

= \frac{0}{1}

Apply rule

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

= 0

y = \frac{x}{x + 9}

\frac{s + 1}{s ^{2} + 3 s + 2}

\frac{\partial}{\partial y} (e^{x} ln (x y))

\int e^{\frac{x}{10}} d x

\int 3 x^{2} + 3 x^{2} ln (y) d x

What is the limit as x approaches infinity of ((sin^2(x)))/(x+e^{-x)} ?
The limit as x approaches infinity of ((sin^2(x)))/(x+e^{-x)} is 0