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Limits Questions

  • Thread starter mathmann
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  • #1
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Homework Statement


Evaluate: lim x(squared) - 2x - 8
x-->4 _________________
x (squareroot of x) -8

Homework Equations





The Attempt at a Solution



subbing 4 in as x resulted in an indterminant.
Ive tried using the conjugate but I get stuck when I can not simplify or cancel.
The main problem I'm having is trying to get rid of the squareroot.
 

Answers and Replies

  • #2
Dick
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What 'conjugate' did you multiply by and what did you get? Show more of your work.
 
  • #3
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mulitplied both num/den by x(squared) + 2x + 8

which resulted x(to the power of 4) - 4x(squared) - 64 on top
but x (squareroot of x) -8 * x(squared) + 2x + 8

can the denominator be simplified more?
 
  • #4
Dick
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Try multiplying top and bottom by x*sqrt(x)+8.
 
  • #5
1,631
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if i got you right, the limit you wrote goes like this

lim (x^2-2x-8)/(x*x^1/2 -8), x-->4 right??
if it is like this than you have to multibly both numerator and denominator by

x*x^1/2+8, what do you get? try this first, than you will get further instructions.

after that try to factorize x^2-2x-8, find x1,x2, what do you get, than on the denominator you get x^3-64, try to factorize this too, and the problem is solved!!

i hope this helps
 
Last edited:
  • #6
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ok i got x(cubed)-2x-64/x(squared)*(x)-64
 
  • #7
Dick
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Not really right. You should still have a sqrt(x) in the numerator. You don't have to multiply the numerator out. The denominator is ok though, factor it.
 
  • #8
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x(cubed)-2x(sqrt(x))-64

is the denominator correct?
 
  • #9
Dick
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If that's supposed to be the numerator, no it's not. It's a binomial times a trinomial - if you do it right you'll get six terms. But I would still encourage you not to do it. Just leave it factored. The denominator IS x^3-64. Have you factored it yet?
 
  • #10
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x(sqrd)-2x-8 * x((sqrt)x) + 8
_________________________

(x-4)((x(sqrd) + 4x + 16)
 
  • #11
Dick
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Ok so far. I'd use more parentheses in the numerator. What do you think you should do now? Hint: the (x-4) term is the source of your problems.
 
  • #12
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I assume theres somewhere that i can reduce but I dont see where.
 
  • #13
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Is the answer 1/24?
 
  • #14
Dick
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Is the answer 1/24?
I doubt it. There's a hidden factor of (x-4) in the numerator. Where could it be?
 
  • #15
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(x-4)(x+2){x(sqrtofx)+8}
_____________________
(x-4){(xsqrd)+4x+16}

the x-4's cancel and then I can sub x = 4?

I got 1/8
 
  • #16
Dick
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Good work! But sub again. Carefully this time.
 
  • #17
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haha whoops 96/48 = 2

Thanks for the help.. much appreciated
 
  • #18
1,631
4
yes after you cancel out the (x-4) you can sub the x for 4, but i still think you got the wrong answer. It should be 2.
 

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