What is the limit as x approaches-infinity of (\sqrt[4]{x^4-3}+6x)/(1-2x) ?

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limit as x approaches-infinity of (\sqrt[4]{x^4-3}+6x)/(1-2x)

x \to - \infty lim (\frac{4 x ^{4} - 3 + 6 x}{1 - 2 x})

- \frac{5}{2}

Decimal

- 2.5

Solution steps

x \to - \infty lim (\frac{4 x ^{4} - 3 + 6 x}{1 - 2 x})

Divide by highest denominator power:

\frac{- 4 1 - \frac{3}{x ^{4}} + 6}{\frac{1}{x} - 2}

= x \to - \infty lim \frac{- 4 1 - \frac{3}{x ^{4}} + 6}{\frac{1}{x} - 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} ( - 4 1 - \frac{3}{x ^{4}} + 6 )}{lim _{x \to - \infty} ( \frac{1}{x} - 2 )}

x \to - \infty lim (- 4 1 - \frac{3}{x ^{4}} + 6) = 5

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

= \frac{5}{- 2}

Simplify

= - \frac{5}{2}

\int p^{3} ln (p) d p

y = x^{4}, y = x^{2}

x \to 4 - lim (\frac{4 x}{x - 4})

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

\int_{2}^{4} (x^{2} + 2)^{3} d x

What is the limit as x approaches-infinity of (\sqrt[4]{x^4-3}+6x)/(1-2x) ?
The limit as x approaches-infinity of (\sqrt[4]{x^4-3}+6x)/(1-2x) is -5/2