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schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1343661876978:dw

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.3Ah! This is one best though of visually, let me make you a graph:

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1If you find the function continuous, then you may just plug 3 for \(x\) by the way.

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1Let's see how the graph is..

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Ok. If I plug in 3, I get 3 sqrt(0)

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.3What you need are numbers slightly less than 3, like 2.9999999999999

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1Looks like we can plug in values less than \(3\).

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1Because it is a left handed limit, we may plug numbers like agentx5 said :)

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.3That  sign above the limit means "numbers from the left hand side limit" or the number slightly less than 3 (but as close as you can get)

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0ok! can you show how I would solve it

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Ok i understand that

telliott99
 2 years ago
Best ResponseYou've already chosen the best response.0About your graph, notice what happens to the function for x > 3

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0So how would I solve the limit?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1By plugging numbers slightly less than 3.

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.3@telliott99 , I know... look at the notation for imaginary and real...

telliott99
 2 years ago
Best ResponseYou've already chosen the best response.0Just saying the graph is not correct. It doesn't have a hole in it. And do what @ParthKohli says

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1\[ \begin{array}{lr} x & f(x) \\ \hline 2.5 & \\ 2.9 \\ 2.999 \\ 2.99999\end{array} \] Fill the f(x)'s.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0for 2.5, f(x) would be 4.145

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.3And and as you get closer and closer to 2.999999999999? Every closer to 3 from the "just under" side and you'll approach some limit.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Ok can you help find the limit now? Like I understand how to find that, i just dont haeve time to find them all

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1Calculator, Schmidt.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0so agentx5, I should just use 2.999999 to find the limit?

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.3Or if you prefer, 2.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999... Get the point? :P

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1Looks like its getting closer to 7.5, but let's see it for more values.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Ok! I think its going to be 7.5

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1Are you sure? Try for 2.9999999 and 2.999999999999999. So on.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0I just tried for that

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0can someone tell me if im right

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1I am too lazy to do so :/

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0plz! i really need your help..

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1All right :) let me check it out on Wolfram.

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1@agentx5 Where is the graph?

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.3Here's the algebra trick, you need to find what y would be when x=3. You can't do this normally but... \(x\sqrt{(3+x)(3x)}\) , For what solutions does y = 0? Well, 0, +3 and 3. So... ;) Replacing with a better graph (more accurate, real #'s only): dw:1343662913297:dw

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0ok thx @agentx5 so what would the limit be for this probb?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1I was actually surprised how I was plugging values and getting it approaching something else. Hence, I asked.

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1The limit was getting smaller and smaller. ;)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1You may find from the graph, actually.dw:1343663313029:dw

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1What is \(y\) approaching in the graph? ^

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.3With the limit shown... dw:1343663226621:dw

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0like 2 or 3 right?

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.3I actually had my imaginary lines going the wrong way @telliott99 and the circles were too high in the original sketch (they're on the xaxis), I stand corrected. Although I'm not sure that's what you meant. ;)

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Guys do you know the actual limit?

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.3And I'm trying to help you learn visually what's going on so you're not lost here

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah I do see it visually,

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0is the limit around 2 or 3

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0wait it looks around 0

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.3\[\lim_{x \rightarrow 3^}\] What is the output of the function approaching? The input gets closer to 3 from the "slightly less" side.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0as 3 approaches 3 from the left, the y value is 0, right?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0sorry i meant, as x approaches 3

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.3Or using the analytical method, as you plug in larger and larger 2.9999999999999999...'s you get smaller and smaller numbers. Infinitesimally small. To the point gets damned close to zero. Thus the limit is zero, correct.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0ok so the limit for this function is 0? :D

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.3The reason you can't just substitute 3 in place of x, officially is because you might have one like this: \[\lim_{x \rightarrow 1} = \frac{1}{1x}\] Look what happens if you plug in 1?

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0But, limit is 0 right? and yes the ddenominator bneomes 0.. not possible

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.3In this case your left and your right hand limits are going in opposite directions, and the limit doesn't exist. dw:1343663845294:dw And yes, twice to the above post. :)

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0wait so the limit is DNE? or zero!?!

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.3For your original problem, Zero. For the one I just asked you, trying to get you to learn, Does Not Exist.

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.3You will see DNE problems, I can guarantee you.

schmidtdancer
 2 years ago
Best ResponseYou've already chosen the best response.0Oh yeah, I know!:)
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