Solve Lim x(squared) - 2x - 8 | x-->4

[mathmann]

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.

 

[Dick]

What 'conjugate' did you multiply by and what did you get? Show more of your work.

 

[mathmann]

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?

 

[Dick]

Try multiplying top and bottom by x*sqrt(x)+8.

 

[sutupidmath]

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

 

[mathmann]

ok i got x(cubed)-2x-64/x(squared)*(x)-64

 

[Dick]

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.

 

[mathmann]

x(cubed)-2x(sqrt(x))-64

is the denominator correct?

 

[Dick]

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?

 

[mathmann]

x(sqrd)-2x-8 * x((sqrt)x) + 8
_________________________

(x-4)((x(sqrd) + 4x + 16)

 

[Dick]

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.

 

[mathmann]

I assume there's somewhere that i can reduce but I don't see where.

 

[mathmann]

Is the answer 1/24?

 

[Dick]

Is the answer 1/24?

I doubt it. There's a hidden factor of (x-4) in the numerator. Where could it be?

 

[mathmann]

(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

 

[Dick]

Good work! But sub again. Carefully this time.

 

[mathmann]

haha whoops 96/48 = 2

Thanks for the help.. much appreciated

 

[sutupidmath]

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.