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

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

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limit as x approaches infinity of (5x)/(7x-4x^3)

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

0

Solution steps

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

Simplify

\frac{5 x}{7 x - 4 x ^{3}} : \frac{5}{7 - 4 x ^{2}}

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 5 \cdot x \to \infty lim (\frac{1}{7 - 4 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

= 5 \cdot \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( 7 - 4 x ^{2} )}

x \to \infty lim (1) = 1

x \to \infty lim (7 - 4 x^{2}) = - \infty

= 5 \cdot \frac{1}{- \infty}

Simplify

5 \cdot \frac{1}{- \infty} : 0

= 0

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