lim_(x→−∞) ((√(x^2 +5x−3))/(10x−3))=???


Question and Answers Forum

All Questions Topic List
Limits Questions
Previous in All Question Next in All Question
Previous in Limits Next in Limits
Question Number 127421 by Study last updated on 29/Dec/20

$l i \underset{x \to - \infty}{m} \frac{\sqrt{x^{2} + 5 x - 3}}{10 x - 3} = ? ? ?$
	Answered by ebi last updated on 29/Dec/20
	$lim_(x→−∞) ((√(x^2 +5x−3))/(10x−3)) =lim_(x→−∞) ((√(x^2 +5x−3))/(10x−3))=lim_(x→−∞) ((√(x^2 (1+(5/x)−(3/x^2 ))))/(x(10−(3/x)))) =lim_(x→−∞) ((∣x∣(√((1+(5/x)−(3/x^2 )))))/(x(10−(3/x)))) =lim_(x→−∞) ((−x(√((1+(5/x)−(3/x^2 )))))/(x(10−(3/x)))), ∣x∣= { ((x, x≥0)),((−x, x<0)) :} =lim_(x→−∞) ((−(√((1+(5/x)−(3/x^2 )))))/((10−(3/x))))=((−(√(1+0−0)))/(10))=−(1/(10))$
	$\underset{x \to - \infty}{l i m} \frac{\sqrt{x^{2} + 5 x - 3}}{10 x - 3}$ $= \underset{x \to - \infty}{l i m} \frac{\sqrt{x^{2} + 5 x - 3}}{10 x - 3} = \underset{x \to - \infty}{l i m} \frac{\sqrt{x^{2} (1 + \frac{5}{x} - \frac{3}{x^{2}})}}{x (10 - \frac{3}{x})}$ $= \underset{x \to - \infty}{l i m} \frac{∣ x ∣ \sqrt{(1 + \frac{5}{x} - \frac{3}{x^{2}})}}{x (10 - \frac{3}{x})}$ $= \underset{x \to - \infty}{l i m} \frac{- x \sqrt{(1 + \frac{5}{x} - \frac{3}{x^{2}})}}{x (10 - \frac{3}{x})}, ∣ x ∣= {\begin{cases} x, x ⩾ 0 \\ - x, x < 0 \end{cases}$ $= \underset{x \to - \infty}{l i m} \frac{- \sqrt{(1 + \frac{5}{x} - \frac{3}{x^{2}})}}{(10 - \frac{3}{x})} = \frac{- \sqrt{1 + 0 - 0}}{10} = - \frac{1}{10}$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum