JS-lim-x-3-5-2x-x-2-x-4-x-2-

Question Number 109861 by john santu last updated on 26/Aug/20

\frac{J S}{★ ★}

\lim_{x \to 3} \frac{5 - 2 x + \sqrt{x - 2}}{x - 4 + \sqrt{x - 2}} ?

Answered by bemath last updated on 26/Aug/20

Commented by john santu last updated on 26/Aug/20

b e a u t i f u l l

Answered by Her_Majesty last updated on 26/Aug/20

\frac{5 - 2 x + \sqrt{x - 2}}{x - 4 + \sqrt{x - 2}} = \frac{6 - 2 x + 3 \sqrt{x - 2}}{x - 6} \Rightarrow l i m = - 1

Commented by bemath last updated on 26/Aug/20

w h a t y o u r m e t h o d m i s s ?

Commented by Her_Majesty last updated on 26/Aug/20

\frac{5 - 2 x + \sqrt{x - 2}}{x - 4 + \sqrt{x - 2}} \times \frac{x - 4 - \sqrt{x - 2}}{x - 4 - \sqrt{x - 2}} =

= \frac{(x - 3) (6 - 2 x + 3 \sqrt{x - 2})}{(x - 3) (x - 6)} = \frac{6 - 2 x + 3 \sqrt{x - 2}}{x - 6}

Commented by bemath last updated on 26/Aug/20

c o o l l \dots . n i c e

Answered by 1549442205PVT last updated on 26/Aug/20

\lim_{x \to 3} \frac{5 - 2 x + \sqrt{x - 2}}{x - 4 + \sqrt{x - 2}} \underset{L^{'} Hopital}{=} \lim_{x \to 3} \frac{- 2 + \frac{1}{2 \sqrt{x - 2}}}{1 + \frac{1}{2 \sqrt{x - 2}}}

= \frac{- 2 + \frac{1}{2}}{1 + \frac{1}{2}} = \frac{- 3 / 2}{3 / 2} = - 1