2. $\lim _{x \rightarrow \infty} \frac{\sqrt{9 x^{4}+1}}{x^{2}-3 x+5}$ is
(A) 1
(B) 3
(C) 9
(D) nonexistent

Question

2. $\lim _{x \rightarrow \infty} \frac{\sqrt{9 x^{4}+1}}{x^{2}-3 x+5}$ is
(A) 1
(B) 3
(C) 9
(D) nonexistent

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the limit of the given function as $ x $ approaches infinity, we can divide the numerator and the denominator by the highest power of $ x $ in the denominator, which is $ x^2 $... ‖ ‖ step 2 ⋮ Simplifying the expression, we get $ \lim_{x \to \infty} \frac{\sqrt{9 + \frac{1}{x^4}}}{1 - \frac{3}{x} + \frac{5}{x^2}} $... ‖ ‖ step 3 ⋮ As $ x $ approaches infinity, the terms $ \frac{1}{x^4} $, $ \frac{3}{x} $, and $ \frac{5}{x^2} $ approach zero... ‖ ‖ step 4 ⋮ The limit then simplifies to $ \lim_{x \to \infty} \frac{\sqrt{9}}{1} $... ‖ ‖ step 5 ⋮ The final result is $ 3 $... ‖ ***B*** ∻Key Concept∻ ⚹Limit of a Rational Function with a Radical as $ x $ Approaches Infinity⚹ ∻Explanation∻ ⚹When finding the limit of a rational function with a radical as $ x $ approaches infinity, divide by the highest power of $ x $ in the denominator and simplify. Terms with $ x $ in the denominator approach zero, and the limit can be evaluated by substituting the remaining terms.⚹◊What is the limit of the given function as $x$ approaches infinity?⍭ Generate me a similar question◊

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