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Limit for basic Calculus I

  • Thread starter alingy1
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  • #1
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lim of (3^y-5^y)/(2^y-7^y) as y->0

Evaluate the above limit.

Okay, so, I was flabbergasted at how challenging this problem is. I realized it was an indeterminate form [0/0]. I was trying to find a way to cancel y out of the numerator and denominator, in vain. I tried finding a pattern to expand the numerator and denominator, in vain: I still ended up with the [0/0].

Any tips?

Please, I have been racking my brains for 3.5 hours. :(
 

Answers and Replies

  • #2
LCKurtz
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lim of (3^y-5^y)/(2^y-7^y) as y->0

Evaluate the above limit.

Okay, so, I was flabbergasted at how challenging this problem is. I realized it was an indeterminate form [0/0]. I was trying to find a way to cancel y out of the numerator and denominator, in vain. I tried finding a pattern to expand the numerator and denominator, in vain: I still ended up with the [0/0].

Any tips?

Please, I have been racking my brains for 3.5 hours. :(
I would start by factoring a ##3^y## out of the numerator and a ##2^y## out of the denominator giving$$
\left (\frac 3 2\right)^y \frac{1-(\frac 5 3)^y}{1 -(\frac 7 2)^y}$$and see if that gives you any ideas.
 
  • #3
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:S
I feel really lost and desperate :S.
I tried taking the (5/3)^y and the (7/2)^y out again. No results. I'm trying to find a way of getting rid of that y.

I have the answer in front of my face: ln5-ln3 over ln7-ln2
I don't see how they get those logs in there :S

Please be patient with my slow mind :P I have been studying from 8AM to 9PM.

EDIT: I BELIEVE I AM GETTING SOMEWHERE. :)
 
Last edited:
  • #4
Dick
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:S
I feel really lost and desperate :S.
I tried taking the (5/3)^y and the (7/2)^y out again. No results. I'm trying to find a way of getting rid of that y.

I have the answer in front of my face: ln5-ln3 over ln7-ln2
I don't see how they get those logs in there :S

Please be patient with my slow mind :P I have been studying from 8AM to 9PM.

EDIT: I BELIEVE I AM GETTING SOMEWHERE. :)
Use your 'special limit'. Have you figured out what lim x->0 (a^x-1)/x is yet? It's 1 if a=e. What is it in general? That's a great place to start.
 
  • #5
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Okay, I am lost.

I made a mistake using the logarithm rules. I came to an answer that was close to the right answer, which excited me a bit. :(

Dick: I just don't see how I could get y at the denominator to use that special limit.
 
  • #6
Dick
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Okay, I am lost.

I made a mistake using the logarithm rules. I came to an answer that was close to the right answer, which excited me a bit. :(

Dick: I just don't see how I could get y at the denominator to use that special limit.
Divide the numerator AND the denominator of LCKurtz's fraction by y. It doesn't change the result, right?
 
  • #7
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Yes, I could find the answer to my previous question. Turns out I didn't need that 'special limit'. Indeed, I just multiplied the denominator and numerator by a^x and that did the trick in me elucidating that daunting question. Sorry I didn't have time to follow up! I have exams this week, so it's rush week!
 
  • #8
Dick
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Yes, I could find the answer to my previous question. Turns out I didn't need that 'special limit'. Indeed, I just multiplied the denominator and numerator by a^x and that did the trick in me elucidating that daunting question. Sorry I didn't have time to follow up! I have exams this week, so it's rush week!
It's fine if you don't have time to follow up. But what did you use instead of the 'special limit'? I don't think just multiplying by a^x will do it. If you think you've got a solution that way it's likely wrong. Just saying...
 
  • #9
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Could you use L'Hopitals?
 
  • #10
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Oh no, do not worry. I got the right answer. Actually, I may have used the 'special limit'. I don't recall. I will have to search through my pile of papers. I'll keep you posted on that.

To answer johnqwertyful, no I cannot. I didn't learn it yet. That's what's making this problem tough :(
 
  • #11
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Nope.
I'm stuck.
(ln3-(ln3)(5/3)^y)/(ln2-(ln3)(7/2)^y)
Same [0/0] story again.
 
  • #12
Dick
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Nope.
I'm stuck.
(ln3-(ln3)(5/3)^y)/(ln2-(ln3)(7/2)^y)
Same [0/0] story again.
Prove a useful result first. As I asked before, what is lim x->0 (a^x-1)/x??
 
  • #13
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1 evidently! :)
 
  • #14
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After 4 hours of sweat, I got it. :) You guys/girls are awesome. :)
 
  • #15
vela
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That's not right. The limit is equal to 1 only if a=e.
 
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