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Question
Evaluate the following:
\[\lim_{x->∞} \frac{2x + 5}{x^2 + 3x + 9}\]
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Solution
\[\lim_{x->∞} \frac{2x + 5}{x^2 + 3x + 9}\]
= \[\lim_{x->∞} \frac{x(2 + \frac{5}x)}{(1 + \frac{3}{x} + \frac{9}{x^2})}\]
[Takeout x from numerator and take x2 from the denominator]
= \[\lim_{x->∞} \frac{1}{x} \frac{(2 + \frac{5}x)}{(1 + \frac{3}{x} + \frac{9}{x^2})}\]
= `0 ((2 + 0)/(1 + 0 + 0))`
= 0
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