What is the limit as x approaches-infinity of \sqrt[3]{((3x^7-4x^5))/(2x^7+1)} ?

The limit as x approaches-infinity of \sqrt[3]{((3x^7-4x^5))/(2x^7+1)} is cube root of 3/2

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limit as x approaches-infinity of \sqrt[3]{((3x^7-4x^5))/(2x^7+1)}

Decimal

1.14471 \dots

Solution steps

Divide by highest denominator power:

\frac{3 - \frac{4}{x ^{2}}}{2 + \frac{1}{x ^{7}}}

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

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

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

x \to - \infty lim (2 + \frac{1}{x ^{7}}) = 2

What is the limit as x approaches-infinity of \sqrt[3]{((3x^7-4x^5))/(2x^7+1)} ?
The limit as x approaches-infinity of \sqrt[3]{((3x^7-4x^5))/(2x^7+1)} is cube root of 3/2