8 votes 8 votes Is there a number $b$ such that $\displaystyle\lim _{x \rightarrow-2} \frac{b x^2+15 x+15+b}{x^2+x-2}$ exists? If so, find the value of $b$ and the value of the limit. $-1$ $-2$ $1$ There is no such $b$ for that above limit exist Calculus goclasses2025_csda_wq8 goclasses calculus limits 2-marks + – GO Classes asked May 24, 2023 • retagged Jun 12 by GO Classes GO Classes 171 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
6 votes 6 votes Detailed Video Solution: https://youtu.be/6aIuj2b2J38 Since the denominator approaches $0$ as $x \rightarrow-2$, the necessary condition for this limit to exist is that the numerator approaches $0$ as $x \rightarrow-2$. Thus we solve $4 b-30+15+b=0$ to obtain $b=3. \displaystyle\lim _{x \rightarrow-2} \frac{3 x^2+15 x+18}{x^2+x-2}=-1$. GO Classes answered May 24, 2023 • edited Sep 1, 2023 by Deepak Poonia GO Classes comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes For making it 0/0 form we have to put numerator equal to zero with the given limit and find the value of b and now put this value into given limit and use L Hopital rule this will give -1 ans ꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂ answered Aug 18, 2023 ꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂ comment Share Follow See all 0 reply Please log in or register to add a comment.
