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)}

x \to - \infty lim (3 \frac{( 3 x ^{7} - 4 x ^{5} )}{2 x ^{7} + 1})

3 \frac{3}{2}

Decimal

1.14471 \dots

Solution steps

x \to - \infty lim (3 \frac{3 x ^{7} - 4 x ^{5}}{2 x ^{7} + 1})

Divide by highest denominator power:

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

= x \to - \infty lim (3 \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

= 3 x \to - \infty lim (\frac{3 - \frac{4}{x ^{2}}}{2 + \frac{1}{x ^{7}}})

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

= 3 \frac{lim _{x \to - \infty} ( 3 - \frac{4}{x ^{2}} )}{lim _{x \to - \infty} ( 2 + \frac{1}{x ^{7}} )}

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

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

= 3 \frac{3}{2}

x \to \infty lim (x ∣ x ∣)

x \to 0 + lim (\frac{7}{x} - \frac{3}{x ^{2}})

x \to 0 lim (cos (x) - x)

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

x \to 0 lim (3^{x + 1} - 3)

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