What is the limit as x approaches infinity of (x-xsqrt(x))/(2x^{3/2)+3x-5} ?

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limit as x approaches infinity of (x-xsqrt(x))/(2x^{3/2)+3x-5}

x \to \infty lim (\frac{x - x x}{2 x ^{\frac{3}{2}} + 3 x - 5})

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

x \to \infty lim (\frac{x - x x}{2 x ^{\frac{3}{2}} + 3 x - 5})

Divide by

x^{\frac{3}{2}} : \frac{\frac{1}{x ^{\frac{1}{2}}} - 1}{2 + \frac{3}{x ^{\frac{1}{2}}} - \frac{5}{x ^{\frac{3}{2}}}}

= x \to \infty lim (\frac{\frac{1}{x ^{\frac{1}{2}}} - 1}{2 + \frac{3}{x ^{\frac{1}{2}}} - \frac{5}{x ^{\frac{3}{2}}}})

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{1}{x ^{\frac{1}{2}}} - 1 )}{lim _{x \to \infty} ( 2 + \frac{3}{x ^{\frac{1}{2}}} - \frac{5}{x ^{\frac{3}{2}}} )}

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

x \to \infty lim (2 + \frac{3}{x ^{\frac{1}{2}}} - \frac{5}{x ^{\frac{3}{2}}}) = 2

= \frac{- 1}{2}

Simplify

= - \frac{1}{2}

9 x + 10

x \to 0 + lim ((x)^{4 x})

\int (\frac{x}{x - 1}) d x

x \to θ lim (x^{2} - 5)

\int \frac{x}{3 + x ^{2}} d x

What is the limit as x approaches infinity of (x-xsqrt(x))/(2x^{3/2)+3x-5} ?
The limit as x approaches infinity of (x-xsqrt(x))/(2x^{3/2)+3x-5} is -1/2