What is the limit as x approaches-infinity of (7x^4-14x^2)/(6x^5+3) ?

The limit as x approaches-infinity of (7x^4-14x^2)/(6x^5+3) is 0

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limit as x approaches-infinity of (7x^4-14x^2)/(6x^5+3)

x \to - \infty lim (\frac{7 x ^{4} - 14 x ^{2}}{6 x ^{5} + 3})

0

Solution steps

x \to - \infty lim (\frac{7 x ^{4} - 14 x ^{2}}{6 x ^{5} + 3})

Divide by highest denominator power:

\frac{\frac{7}{x} - \frac{14}{x ^{3}}}{6 + \frac{3}{x ^{5}}}

= x \to - \infty lim (\frac{\frac{7}{x} - \frac{14}{x ^{3}}}{6 + \frac{3}{x ^{5}}})

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{7}{x} - \frac{14}{x ^{3}} )}{lim _{x \to - \infty} ( 6 + \frac{3}{x ^{5}} )}

x \to - \infty lim (\frac{7}{x} - \frac{14}{x ^{3}}) = 0

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

= \frac{0}{6}

Apply rule

\frac{0}{a} = 0, a \neq = 0

= 0

\frac{d}{d x} (sin (\frac{5}{2} ln (x)))

\int \frac{sin ( k t )}{a + cos ( k t )} d t

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

x \to 0 lim (\frac{x - 2}{x - 2})

\frac{\partial}{\partial y} (e^{- x} sin (y))

What is the limit as x approaches-infinity of (7x^4-14x^2)/(6x^5+3) ?
The limit as x approaches-infinity of (7x^4-14x^2)/(6x^5+3) is 0