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Problem 9 Easy Difficulty

For the function $ f $ whose graph is shown, state the following.

(a) $ \displaystyle \lim_{x\to -7}f(x) $
(b) $ \displaystyle \lim_{x\to -3}f(x) $
(c) $ \displaystyle \lim_{x\to 0}f(x) $
(d) $ \displaystyle \lim_{x\to 6^-}f(x) $
(e) $ \displaystyle \lim_{x\to 6^+}f(x) $
(f) The equations of the vertical asymptotes.

Answer

(a) $\lim _{x \rightarrow-7} f(x)=-\infty$
(b) $\lim _{x \rightarrow-3} f(x)=\infty$
(c) $\lim _{x \rightarrow 0} f(x)=\infty$
(d) $\lim _{x \rightarrow 6^{-}} f(x)=-\infty$
(e) $\lim _{x \rightarrow 6^{+}} f(x)=\infty$
(f) The equations of the vertical asymptotes are $x=-7, x=-3, x=0,$ and $x=6$.

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Video Transcript

in this problem it is given that for the function f who's graph is shown? Stately following. Right? So we need to find all the parts Right? So here here grab is given so let us see that is compared So at X is equal to -7. What is the value of? Why here I fix is nothing but value of why? So it is nothing but this is minus infinity because we are not getting any value sometimes not Right? So this is minus infinity Okay, now moving forward Here we can see extends to -3 for FX the limit will be what the value will be. What? Yeah so extend to minus t again here we can see there is plus infinity this post minus infinity remember but this was plus infinity Okay so this is going to plus infinity this will be plus infinitely No, for the 3rd part X for limit extends to zero of FX will give me what? Well it will give us Yeah Extends to zero again so this will be plus infinity can we say this? Yes, so this will be plus infinity remember I'm not able to right here. Okay this is a b plus infinity Okay, so the value will be plus infinity again here moving forward, why extends to six minus the value for fx will be 16 minus cities asked Okay, so for six minus the value is minus infinity because from six minus if we see this curve is coming so this is coming down so this will be minus infinity. Alright, so the value for it limit Extends to mine 6- will be minus that reflect their. Yeah. Okay now for six plus it is a fast for for six plus six plus it should be uh the uh something which is in sixth place there should be plus infinitely. This girl is coming. Okay so this should be plus infinity plunge age. So here vertical ACM toads are there then it is us for vertical essentials. So the smallest values asked then largest value is us. Right? So the smallest where you will be from, the smallest. I'm writing from the smallest. Two largest. Right, so this will be X equals two minus seven. Here. S symptoms and s and thoughts are there then minus three. Is that right? In increasing order than X equals to zero. Is also here then We can see at S. X. Z. equals two six. So this is how we arrange from the uh huh. From the smallest value. Two largest value for the vertical ascent. So this will be X. Then this is the first, this is second, this is third and quote. So what will be that? That will be X equals two minus three. X equals two years. Zero. And again, exit was 26 year. So this will be the largest. So in this way we do this question. I hope your industry the cancer. Thank you for watching