Question

find the lim as x approaches 25 for sqrt x -5 / x-25

I get the indeterminate form of 0/0 and I know thats wrong
But I don't know what to do from there

Answer 1

can you rationalize the numerator ?

Answer 2

the sqrt only covers x

Answer 3

I think thats what I'm supposed to do but I honestly don't know how

Answer 4

How do I start?

Answer 5

Use L'hopital's Rule. That's my suggestion.

Answer 6

multiply numerator and denominator by the conjugate of sqrt x - 5
which is \(\sqrt x+5 \)

Answer 7

But you'll get a sqrt in the denominator @hartnn

Answer 8

the bottom is a difference of squares

Answer 9

ok I am very confused right now.... :/

Answer 10

thats ok, and yes, we can factor denominator too as amistre said

Answer 11

wouldn't a difference of squares work if x^2-25? @amistre64

Answer 12

@hartnn What about L'hopital's?

Answer 13

any number can be squared ....

Answer 14

\[(\sqrt{x})^2-5^2\]

Answer 15

if L'Hopitals can be used, then its easy, but lets not use it, lets do it without that rule

Answer 16

so I can put that in the denominator?

Answer 17

@amistre64

Answer 18

If you say so ^_^

Answer 19

you can yes, and then you can see that the top and bottom have like factors

Answer 20

ok @hartnn

Answer 21

LHop is good, but only if the student has covered it in class. For some reason, teachers fuss at you if you know more than they teach :)

Answer 22

i think you guys will handle this, i'll go help others...

Answer 23

right so there are like factors and I can cancel out

Answer 24

correct, you cancel out the "hole" and simplify the setup to an equivalent construction

Answer 25

@amistre64 You have a point there... It's weird isn't it... So much of independent learning. That's why I prefer home-schooling...

Answer 26

Gauss would never have made it in our day and age lol

Answer 27

I agree...

Answer 28

so would it become sqrt x - 5?

Answer 29

as in you cancel out the top and you get that in the denominator?

Answer 30

\[\frac{\sqrt x-5}{x-25}\]
\[\frac{\cancel{\sqrt x-5}}{\cancel{(\sqrt x-5)}(\sqrt x+5)}\]

Answer 31

1/(sqrt(x)+5) if we do it right ;)

Answer 32

got it

Answer 33

so now would I insert 25?

Answer 34

or leave it like that?

Answer 35

id insert the 25 to see what the value of the limit would be.

Answer 36

"find the lim" assume we want a definite value of some sort, the proces we took just gets us to a point that is not undeterminate is all

Answer 37

ok so 1/ sqrt 25+5 = 1/5.5 ?

Answer 38

1/(5+5) is how i see it

Answer 39

oh your right because the sqrt only covers x

Answer 40

:)

Answer 41

so the lim is 1/10

Answer 42

Yep

Answer 43

correct

Answer 44

@amistre64 L'Hopital's a great cheat code to bypass so many things lol

Answer 45

Thank you guys so much, could I post another question?

Answer 46

Sure

Answer 47

It's a graph I don't know how to do

Answer 48

new questons are best posted as a new post

Answer 49

i will