Without-using-l-hopital-find-lim-x-3-9-x-2-x-3-

Question Number 39078 by Cheyboy last updated on 02/Jul/18

W i t h o u t u s i n g l^{'} h o p i t a l

f i n d \lim_{x \to 3} \frac{\sqrt{9 - x^{2}}}{x - 3}

Commented by math khazana by abdo last updated on 03/Jul/18

{l i m}_{x \to 3^{-}} \frac{\sqrt{9 - x^{2}}}{x - 3} = {l i m}_{x \to 3^{-}} - \frac{\sqrt{9 - x^{2}}}{3 - x}

= {l i m}_{x \to 3^{-}} - \sqrt{\frac{9 - x^{2}}{{(3 - x)}^{2}}} = {l i m}_{x \to 3^{-}} - \sqrt{\frac{3 + x}{3 - x}}

= - \infty .

Commented by orlandorap123 last updated on 03/Aug/18

\lim_{x \to 3} \frac{\sqrt{9 - x^{2}}}{x - 3}

\lim_{x \to 3} \frac{(3 - x) (3 + x)}{- (x - 3) \sqrt{9 - x^{2}}}

\lim_{x \to 3} \frac{(3 + x)}{- \sqrt{9 - x^{2}}}

evaluando

\lim_{x \to 3} \frac{(6)}{- 0} = - \infty

f i n d \lim_{x \to 3} \frac{\sqrt{9 - x^{2}}}{x - 3} = - \infty

Answered by ajfour last updated on 02/Jul/18

l e f t h a n d l i m i t = \lim_{h \to 0} \frac{\sqrt{9 - {(3 - h)}^{2}}}{(3 - h) - 3}

= \lim_{h \to 0} \frac{\sqrt{6 h - h^{2}}}{- h} = - \infty

Commented by Cheyboy last updated on 02/Jul/18

T h a n k y o u s i r

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