What is the limit as x approaches infinity of (10x+100)/(x^2-30) ?

The limit as x approaches infinity of (10x+100)/(x^2-30) is 0

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limit as x approaches infinity of (10x+100)/(x^2-30)

x \to \infty lim (\frac{10 x + 100}{x ^{2} - 30})

0

Solution steps

x \to \infty lim (\frac{10 x + 100}{x ^{2} - 30})

Divide by highest denominator power:

\frac{\frac{10}{x} + \frac{100}{x ^{2}}}{1 - \frac{30}{x ^{2}}}

= x \to \infty lim (\frac{\frac{10}{x} + \frac{100}{x ^{2}}}{1 - \frac{30}{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

= \frac{lim _{x \to \infty} ( \frac{10}{x} + \frac{100}{x ^{2}} )}{lim _{x \to \infty} ( 1 - \frac{30}{x ^{2}} )}

x \to \infty lim (\frac{10}{x} + \frac{100}{x ^{2}}) = 0

x \to \infty lim (1 - \frac{30}{x ^{2}}) = 1

= \frac{0}{1}

Apply rule

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

= 0

What is the limit as x approaches infinity of (10x+100)/(x^2-30) ?
The limit as x approaches infinity of (10x+100)/(x^2-30) is 0