Evaluate-i-lim-x-2-3x-3-4x-2-ii-lim-x-2-3x-3-4x-2-

Question Number 28876 by Rasheed.Sindhi last updated on 31/Jan/18

E v a l u a t e

(i) \underset{x \to - \infty}{l i m} \frac{2 - 3 x}{\sqrt{3 + {4 x}^{2}}}

(ii) \underset{x \to + \infty}{l i m} \frac{2 - 3 x}{\sqrt{3 + {4 x}^{2}}}

Commented by abdo imad last updated on 31/Jan/18

i) = {l i m}_{x \to - \infty} \frac{2 - 3 x}{\sqrt{4 x^{2} (1 + \frac{3}{4 x^{2}})}} = {l i m}_{x \to - \infty} \frac{- 3 x + 2}{2 ∣ x ∣ \sqrt{1 + \frac{3}{4 x^{2}}}}

= {l i m}_{x \to - \infty} \frac{- 3 x + 2}{- 2 x} = \frac{3}{2}

i i) = {l i m}_{x \to + \infty} \frac{- 3 x + 2}{2 ∣ x ∣ \sqrt{1 + \frac{3}{x^{2}}}} = {l i m}_{x \to + \infty} \frac{- 3 x + 2}{2 x} = - \frac{3}{2} .