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Lizzie

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Sep 8, 2005
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This isn't urgent, but if anyone could check this out since I have noone else to ask, I'm just trying to find out if I'm doing this right.

a) lim as x :arrow: -3 of (x<sup>2</sup>-x-12)/(x+3) = -7

b) lim as x :arrow: 8 of (3x-7x)<sup>2</sup> = -424 (not sure about that one)

c) lim as h :arrow: 0 of ((2+h)<sup>3</sup>-8)/h = (I thought that I knew how to do this one, but I guess I don't. If I knew where to start I should be able to get it.)
 
a) Yes.

b) There aren't any domain problems; this is just a polynomial. So all you have to do is evaluate.

c) Try multiplying it out. Once you simplify, you'll be able to cancel out the "h" in the denominator, and then just plug-n-chug to get the answer.

Eliz.
 
I'm sorry, but I don't understand what you mean for b. I think you said I did it wrong, but I don't know how. Sorry.
 
b) Is there any "division by zero" problem? Any "negative inside the square root" problem? Is there anything that requires tricks or fancy footwork? Or is this just a polynomial, so you're just plugging in for x?

(I think you're over-thinking this. But this is a polynomial. It's the easy case. Just plug-n-chug.)

Eliz.
 
What I did for b was substituted the limit, that's how i got that number
 
am i supposed to do it differently? I'm seriously clueless, sorry. Oh and thanks for the start on c :)
 
How can you "substitute" the limit? You're trying to find the limit. (And (-4×8)<sup>2</sup> does not equal -424.)

Eliz.
 
What am I supposed to do then? I thought that's what i was supposed to do. I did that for a...
 
man, i should change my screen name to seriously_confused_n_annoying, lol. I've got to be getting on your nerves by now.
 
You're "supposed to do" exactly what I've said: Evaluate the polynomial at the given x-value. Simplify to find the limit value.

Eliz.
 
I'm sorry that I'm not understanding how you're saying this to me but please don't bite my head off. I'm trying to understand you and I'm getting discouraged. If I'm annoying you, please just tell me and I will try to find the answer some other way.
 
I'm sorry, but I don't understand what is confusing you. You're evaluating; you're plugging the "8" in for the "x", and simplifying to get the limit. You have (3x - 7x)<sup>2</sup> = (-4x)<sup>2</sup>, and you're plugging "8" in for the "x" to get "(-4×8)<sup>2</sup>", and then you're plugging that into your calculator to get the answer.

Where am I losing you on this?

Eliz.
 
OK, I did that. I put in 8 for x. (3(8)-7(8)<sup>2</sup>) Then, when I solved it, it came out to be that number...Do you see where I am going wrong? The reason I wasn't understanding you is because I was doing what you told me to do, we were just calling it different thing, so I am sorry too.
 
You gave the expression earlier as being "(3x - 7x)<sup>2</sup>". Now you are saying that the expression is "3x - 7x<sup>2</sup>", I think. If the expression is something different, then, yes, the limit will likely be something different.

Eliz.
 
Oh man...sorry, here is the exact way it is written...
lim as x :arrow: 8 of (3x-7x<sup>2</sup>
So, did I do it right?

and, for c, which you definitely helped me out on, I got
lim as h :arrow: 0 = 12???
 
I am so very sorry about that. That right there explains our confusion, frustration, and your impatience with me. I'm sorry.
 
b) With the new expression, yes, the limit is -424.

c) Yes, the limit is "12". (And, when they start taking you through derivatives and their formulas, you will be able to look back and recognize this as being "the derivative of x<sup>3</sup>, evaluated at x = 2".)

Eliz.
 
wow, i should have seen that before, I really appreciate your help. You have no idea. I am taking an online class and it's my first college course. The professor, well, let's just say I've never had ANY interection with him AT ALL. So, I'm basically trying to teach myself calc and failing miserably. Also, This thing is due monday...the day my fiance leaves for the Navy, so obviously I'm kinda a basket-case at this point. Thank you so much!! Sorry for the misunderstanding.
 
S'okay. Just take this as a "head's up" to get good at proof-reading your work. (I had to learn this lesson the hard way, too; you're not alone. Just be glad you're learning on a tutoring forum, and not on a test.) (Don't ask. Let's just say that I was very grateful that the teacher was a gentle grader.)

I've heard that online math is very difficult. You have my sympathies. Just try to stay on top of things, and don't be shy about asking questions as soon as you have them. You don't want to get behind, because the new stuff is always building on the old. Come by when you need some assistance. Post clearly and completely, and you should generally get fairly helpful replies.

Eliz.
 
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