Evaluate the limit by change of variable

  • Thread starter p.ella
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  • #1
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Hey everyone :) Got stuckon a calc question and needed some help, my test is coming up :S Please & thankyouu!! Here's the question:

Evauate the limit by change of variable:

lim (x-->4) [(x^1/2)-2] / [(x^1/3)-8]

The answer in the back of the book is 1/12. It MAY be wrong though.

Here's my attempt:

let u= x^1/3
u^3= x
as x-->4 u^3--->4 u--->4^1/3

lim (u--->4^1/3) [(u^3/2)-2] / u-8

That's as far as I could get. Any help asap would be much much MUCH appreciated! cheers yall!
 

Answers and Replies

  • #2
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Go to the 7min mark
 
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  • #3
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Go to the 7min mark

Tried watching but still a bit confused :S how do you know which exponents to raise the new variabe to? (In the video)
 
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  • #4
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Have you learned the properties of limits yet? One of them is that the limit of a fraction is the limit of the numerator over the limit of the denominator. In fact, you could have solved it right from the beginning without doing any substitution.
 
  • #5
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Have you learned the properties of limits yet? One of them is that the limit of a fraction is the limit of the numerator over the limit of the denominator. In fact, you could have solved it right from the beginning without doing any substitution.

Yes I have learned the properties but wasn't sure how to use them in this particular question. Could you maybe show how they work with this problem? Even if it's just the first few steps? Thankyou :) If not I totally understand :)
 
  • #6
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Just do exactly what I said. Take the limit of the numerator as ##x \to 4## and the denominator as ##x \to 4##. Remember that whenever you have a limit tending to 0 over something that's not 0, the limit evaluates to 0. (Well, in this case at least.)
 
  • #7
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Just do exactly what I said. Take the limit of the numerator as ##x \to 4## and the denominator as ##x \to 4##. Remember that whenever you have a limit tending to 0 over something that's not 0, the limit evaluates to 0. (Well, in this case at least.)

I shall try and let you know what I get! Thanlyou for the help :)
 

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