What is the limit as x approaches-infinity of (-10x^5-7x^3)/(5+2x^5) ?

The limit as x approaches-infinity of (-10x^5-7x^3)/(5+2x^5) is -5

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limit as x approaches-infinity of (-10x^5-7x^3)/(5+2x^5)

x \to - \infty lim (\frac{- 10 x ^{5} - 7 x ^{3}}{5 + 2 x ^{5}})

- 5

Solution steps

x \to - \infty lim (\frac{- 10 x ^{5} - 7 x ^{3}}{5 + 2 x ^{5}})

Divide by highest denominator power:

\frac{- 10 - \frac{7}{x ^{2}}}{\frac{5}{x ^{5}} + 2}

= x \to - \infty lim (\frac{- 10 - \frac{7}{x ^{2}}}{\frac{5}{x ^{5}} + 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} ( - 10 - \frac{7}{x ^{2}} )}{lim _{x \to - \infty} ( \frac{5}{x ^{5}} + 2 )}

x \to - \infty lim (- 10 - \frac{7}{x ^{2}}) = - 10

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

= \frac{- 10}{2}

Simplify

= - 5

x \to \infty lim (4 x - 2)

x \to 2 lim (14)

x \to 0 + lim ((x + 1) ln (x))

x \to 3 lim ((5 x^{2})^{0})

x \to 4 lim (a x^{2} + b x + 4)

What is the limit as x approaches-infinity of (-10x^5-7x^3)/(5+2x^5) ?
The limit as x approaches-infinity of (-10x^5-7x^3)/(5+2x^5) is -5