# Thread: Indeterminate Limits, Help! lol

1. ## Indeterminate Limits, Help! lol

I've got a HW problem I just cannot figure out. Can someone please explain how to solve this. I know it is a indeterminate limit and I was told to use algebraic laws to solve it, but my algebra is a little rusty.

Lim x->4 ( ( 1/sqrt(x)-2 ) - ( 4/x-4 ) ) ?
I know the answer is 1/4, but have no idea how that is the answer.

also,

Lim x->0 ( ( 3^(2x)-1 ) / ( 3^(x) -1 ) )

Thank you to anyone can help me with these two problems!

2. Hello,
Originally Posted by gandrade3
I've got a HW problem I just cannot figure out. Can someone please explain how to solve this. I know it is a indeterminate limit and I was told to use algebraic laws to solve it, but my algebra is a little rusty.

Lim x->4 ( ( 1/sqrt(2)-2 ) - ( 4x-4 ) )?
I know the answer is 1/4, but have no idea how that is the answer.
huh ?
Is it $\displaystyle \lim_{x \to 4} \frac{\frac{1}{\sqrt{2}}-2}{4x-4}$ ?

also,

Lim x->0 ( ( 3^(2x)-1 ) / ( 3^(x) -1 ) )

Thank you to anyone can help me with these two problems!
Note that $\displaystyle 3^{2x}=(3^x)^2$

now you have a difference of squares in the numerator. So factorise

3. No, sorry about the confusion. I was in a rush and made some mistakes on the first.

Lim x->4 ( ( 1/sqrt(x)-2 ) - ( 4/x-4 ) )

I forgot to put the division sign between 4 and x-4. (1/sqrt(x)-2) and (4/x-4) are subtracted by each other.

4. Originally Posted by gandrade3
No, sorry about the confusion. I was in a rush and made some mistakes on the first.

Lim x->4 ( ( 1/sqrt(x)-2 ) - ( 4/x-4 ) )

I forgot to put the division sign between 4 and x-4. (1/sqrt(x)-2) and (4/x-4) are subtracted by each other.
Sorry, I misread and put a division sign instead of -.

Multiply the first fraction by $\displaystyle \frac{\sqrt{x}+2}{\sqrt{x}+2}$ ($\displaystyle {\sqrt{x}+2}$ is the conjugate of $\displaystyle {\sqrt{x}-2}$)

Then you'll have to be careful, take 2 situations :
- $\displaystyle x \to 4$ and x>4
- $\displaystyle x \to 4$ and x<4