What is the limit as x approaches infinity of (-1^{x+1}x)/(x+sqrt(x)) ?

The limit as x approaches infinity of (-1^{x+1}x)/(x+sqrt(x)) is -1

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limit as x approaches infinity of (-1^{x+1}x)/(x+sqrt(x))

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

- 1

Solution steps

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

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

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

Simplify

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

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

Divide by

x : \frac{1}{1 + \frac{1}{x}}

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

x \to \infty lim (1) = 1

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

= - \frac{1}{1}

Simplify

= - 1

\int \frac{sin ( 2 x )}{39 + cos ^{2} ( x )} d x

f (x) = sin (x^{2} + x)

x y^{^{'}} = - y - x

x \to 5 lim (\frac{x + 1}{x + 5})

\int sin^{7} (θ) cos^{5} (θ) d θ

What is the limit as x approaches infinity of (-1^{x+1}x)/(x+sqrt(x)) ?
The limit as x approaches infinity of (-1^{x+1}x)/(x+sqrt(x)) is -1