A community for students.
Here's the question you clicked on:
 0 viewing
mathcalculus
 2 years ago
Evaluate the limit: can someone explain me this?
(attached below)
mathcalculus
 2 years ago
Evaluate the limit: can someone explain me this? (attached below)

This Question is Closed

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0when we evaluate the limit, do we not substitute?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0this is where i'm confused.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0in this case, i got the answer right. i kind of took a smart guess

pgpilot326
 2 years ago
Best ResponseYou've already chosen the best response.1at x=11/8 the bottom goes to 0, right? But coming from the right, the bottom is neg, as is the top so it goes to inf. Coming from the left, the bottom is pos and the top is neg so it goes to minf. Make sense?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0When the limit is NOT giving you an indeterminate form, yes you're allowed to substitute the value directly in :)

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0@pgpilot326 a little

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0indeterminate form meaning.... 0/0?

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.0You're really just testing points on each side of your undefined point. You need to see what the behavior is on each side, so pick a point on each side and see what it's doing.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i got the numerator..319/8 and the denominator 77/8

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.0And indeterminate form can mean more than just 0/0. For the purposes of calc 1, yeah, 0/0

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i simply subtracted and simplified.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0but i saw that they asked infinity or non infinity etc etc

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah, because it will go to infinity or negative infinity. You're approaching an asymptote, not an actual point. The graph will just shoot up or down. But the way to see whether it shoots up or down is to test points on each side of the asymptote.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0so what i did was wrong?

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.0Kinda, yeah. I would just pick a point really close to the asymptote on each side. If it's really close, your number will either be really high in the positive direction or really high in the negative direction.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0so.... how should i do it?

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.0Like I picked the number 5/4 for the left side and got 145/4. Picking 3/2 for the right side I got 87/2. You can kinda see how one gets high fast and one goes low fast.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0im more confused now. :/

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.0I would just personally pick numbers on each side of the asymptote that are very close to it. If they're close enough, the answer should tell you pretty clearly if you're going way negative or way positive. Maybe the others can explain better x_x

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0yeah what if i wanted to use 11/8

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0it's kidn of the same thing... right?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i see that one goes really high up and the other goes really down.

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.0Then you will get an undefined answer. An undefined answer does you no good.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0no i didn't get an undefined answer...

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.0Oh, I apologize, I did not look correctly. I'm brain cramping then, ignore what I've said x_x

pgpilot326
 2 years ago
Best ResponseYou've already chosen the best response.1look, when x is near 11/8 but more, 11  8x is gonna be negative. neg over neg is pos. when x is near 11/8 but less, 11  8x is gonna be pos. neg over pos is neg. In both cases, 11  8x is headed towards 0 as x goes to 11/8.

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.0Wait, what? You DIDNT get an undefined? 11 8(11/8)?

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.0I guess I was right and confused myself _ Well, my advice would to just do what I tried to explain. If you can test points on both sides of the asymptote and see theyre really positive or really negative, that you should tell you your answer. As to how you didn't get an undefined when you plugged in 11/8, I'm not sure?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0@pgpilot326 show it pls

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah. nvm, I'm clearly being confusing. I'll leave, sorry.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0#1) can i simply substitute 11/8 into the equation? yes or no?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0okay no, this method confused me from the beginning. :/

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0@zepdrix wait what?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0lemme erase all that nonsense and see if i can explain this :)

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0\[\large \lim_{x\to11/8^+} \frac{29x}{118x} \qquad\to\qquad \frac{39.875}{0}\] Plugging the fraction directly in shows us that we're approaching this form. Since we're approaching a zero in the denominator, it means there's an asymptote at x=11/8. We need to figure something out though. Are we approaching positive or negative infinity? Well our numerator is negative. How about our denominator? When x is a tiny bit bigger than 11/8, is the denominator negative or positive?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0@zepdrix how'd you get that number?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0I plugged 11/8 directly in.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0oh ok i see where you got the number from

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0negative? Is that in response to the question about the denominator?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i think, not sure. i think it's negative.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, very good! Because \(\large 8x\) is slightly larger than \(\large 11\) when we plug in a value larger than 11/8. So \(\large 118x\) is giving us a negative value when we approach from the larger side.

pgpilot326
 2 years ago
Best ResponseYou've already chosen the best response.1think of the function 1/x. when x goes to zero, the function goes to inf from the right because x is positive and it goes to negative infinite from the left because x is negative. the limit doesn't exist because it goes to 2 different places when coming from the left and right. You're problem is the same except it goes to 0 on the bottom when x =11/8. So the limit won't exist at x=11/8 if the limit goes to 2 different places coming from the left and right. 118x=0 when x=11/8. But if x>11/8, 118x is negative and if x<11/8, 118x is positive. This is how you determine where it's heading as you approach the zero from either side.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0^ yah make sure you're comfortable with \(\large \lim_{x\to0}\dfrac{1}{x}\) as pilot explained.

pgpilot326
 2 years ago
Best ResponseYou've already chosen the best response.1But don't forget what the top is doing too.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0okay, so what are the exact rules to every limit problem. keeping in mind y/x if denominator is 0 then it's negative?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i know this: ex: 1/x all real numbers except x=0

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0with this problem. im just so so confused on to how to approach it.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0ex: step by step. and the understanding part is the hardest part.

pgpilot326
 2 years ago
Best ResponseYou've already chosen the best response.1\[\lim_{x \rightarrow a}f \left( x \right)=c \iff \lim_{x \rightarrow a ^{+}}f \left( x \right)=\lim_{x \rightarrow a ^{}}f \left( x \right)=c\] This says the limit exists if and only if the limit from the left and right are the same. You can have different left and right limits, in which case the overall limit will not exist. For example, let \[f \left( x \right)=\frac{ 1 }{ \left( x3 \right) }\] in order to determine \[\lim_{x \rightarrow 3}f \left( x \right)\] we need to look at what happens on the left and right as x approaches 3. \[\lim_{x \rightarrow 3^{+}}\frac{ 1 }{ \left( x3 \right) }=+\infty\]because \[\left( x3 \right)>0, \forall x>3\]. Likewise, \[\lim_{x \rightarrow 3^{}}\frac{ 1 }{ \left( x3 \right) }=\infty\]because \[\left( x3 \right)<0, \forall x<3\]. The bottom is going to 0 as x gets closer and closer to 3. But coming from above 3 (like 3.1, 3.01, 3.001), the bottom is still positive as it goes to zero. yetcoming from below 3 (like 2.9, 2.99, 2.999) the bottom is still negative as it goes to zero. I hope that helps cause it was alot to type.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0thanks i understand it much better.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i see that the left side is coming from the negative side. and right from the positive.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0now let's say for this problem:

pgpilot326
 2 years ago
Best ResponseYou've already chosen the best response.1For all of these evaluate the top and bottom separately and them bring them together. the bottom is always positive, no matter what side you come from. That's because you're squaring the bottom. The top is always going to be negative. Thus all of them will be negative infinity. Do you see?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i substituted all 7 in.... the problem is the signs right and left.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i typed in n, p, dne

pgpilot326
 2 years ago
Best ResponseYou've already chosen the best response.1You can break up the limit into the limit of the top times the limit of the bottom. If the limit exists in each case, then all of the limits (left, right and overall) will be the same. \[\lim_{x \rightarrow 7}\left( \frac{ 2x+1 }{ \left( x7 \right)^{2} } \right)=\lim_{x \rightarrow 7}\left( 2x+1 \right) \times \lim_{x \rightarrow 7}\left( \frac{ 1 }{ \left( x7 \right)^{2} } \right)\] \[\lim_{x \rightarrow 7}2x+1 = 13 \iff \lim_{x \rightarrow 7^{}}2x+1 =\lim_{x \rightarrow 7^{+}}2x+1 = 13\] Also \[\lim_{x \rightarrow 7}\left( \frac{ 1 }{ \left( x7 \right)^{2} } \right)=+\infty \iff \lim_{x \rightarrow 7^{}}\left( \frac{ 1 }{ \left( x7 \right)^{2} } \right)=\lim_{x \rightarrow 7^{+}}\left( \frac{ 1 }{ \left( x7 \right)^{2} } \right)=+\infty\] So \[\lim_{x \rightarrow 7}\left( \frac{ 2x+1 }{ \left( x7 \right)^{2} } \right)=\infty \iff \lim_{x \rightarrow 7^{}}\left( \frac{ 2x+1 }{ \left( x7 \right)^{2} } \right)=\lim_{x \rightarrow 7^{+}}\left( \frac{ 2x+1 }{ \left( x7 \right)^{2} } \right)=\infty\]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.