Problem to solve
Compute \[ \lim_{ x \to \infty } \frac{\sqrt{x^2+5}}{3x^2-2} \]
Solution
STEP 1
Find the following limit: lim_(x->∞) sqrt(x^2 + 5)/(3 x^2 - 2)
STEP 2
Hint: | The degree of the numerator of sqrt(x^2 + 5)/(3 x^2 - 2) is lower than that of its denominator, so it grows asymptotically slower as x approaches ∞. Since sqrt(x^2 + 5) grows asymptotically slower than the polynomial 3 x^2 - 2 as x approaches ∞, lim_(x->∞) sqrt(x^2 + 5)/(3 x^2 - 2) = 0: Answer: | | 0
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Edited by tododemate® - 2021