Thread: hwo to evaluate these limits?!

1. hwo to evaluate these limits?!

how would i evaluate these two limits? they're on my textbook but half of the page is ripped off with the answers..

lim x-16 / (quad root of x) - 2
x -> 16

and

lim (square root of 1-x) - 1 / (square root of 4-x) - 2
x -> 0

i'm not sure if it's called "quad" root, sorry!

thanks!

2. Originally Posted by kelvinly
how would i evaluate these two limits? they're on my textbook but half of the page is ripped off with the answers..

lim x-16 / (quad root of x) - 2
x -> 16

and

lim (square root of 1-x) - 1 / (square root of 4-x) - 2
x -> 0

i'm not sure if it's called "quad" root, sorry!

thanks!
for the first limit ...

$\displaystyle x-16 = (\sqrt{x}+4)(\sqrt{x}-4) = (\sqrt{x}+4)(\sqrt[4]{x}+2)(\sqrt[4]{x}-2)$

for the second limit, rationalize numerator and denominator ...

$\displaystyle \displaystyle \frac{\sqrt{1-x}-1}{\sqrt{4-x}-2} \cdot \frac{(\sqrt{1-x}+1)(\sqrt{4-x}+2)}{(\sqrt{1-x}+1)(\sqrt{4-x}+2)}$

3. Is there a way to do like mathtype style stuff here?

4. Originally Posted by Knukles
Is there a way to do like mathtype style stuff here?
yes. see the LaTeX tutorials here