What is the limit as x approaches infinity of (100x^4-5x^3+1)/(2-2x^2-10x^4) ?

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limit as x approaches infinity of (100x^4-5x^3+1)/(2-2x^2-10x^4)

x \to \infty lim (\frac{100 x ^{4} - 5 x ^{3} + 1}{2 - 2 x ^{2} - 10 x ^{4}})

- 10

Solution steps

x \to \infty lim (\frac{100 x ^{4} - 5 x ^{3} + 1}{2 - 2 x ^{2} - 10 x ^{4}})

Divide by highest denominator power:

\frac{100 - \frac{5}{x} + \frac{1}{x ^{4}}}{\frac{2}{x ^{4}} - \frac{2}{x ^{2}} - 10}

= x \to \infty lim (\frac{100 - \frac{5}{x} + \frac{1}{x ^{4}}}{\frac{2}{x ^{4}} - \frac{2}{x ^{2}} - 10})

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} ( 100 - \frac{5}{x} + \frac{1}{x ^{4}} )}{lim _{x \to \infty} ( \frac{2}{x ^{4}} - \frac{2}{x ^{2}} - 10 )}

x \to \infty lim (100 - \frac{5}{x} + \frac{1}{x ^{4}}) = 100

x \to \infty lim (\frac{2}{x ^{4}} - \frac{2}{x ^{2}} - 10) = - 10

= \frac{100}{- 10}

Simplify

= - 10

z \to 0 lim (\frac{z}{z})

x \to 0 lim (x^{3} ln (4 x))

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

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

h \to 0 lim (h - 2)

What is the limit as x approaches infinity of (100x^4-5x^3+1)/(2-2x^2-10x^4) ?
The limit as x approaches infinity of (100x^4-5x^3+1)/(2-2x^2-10x^4) is -10