Question

evaluate the limit as x goes to 121: (attached with radical in denom)

Answer 1

I rationalized the radical. but it still landed up as DNE

Answer 2

oooh, isee what I did wrong

Answer 3

no limit if that is really the problem

Answer 4

do you use sqrt(x)-11 to rationalize? or

Answer 5

denominator goes to zero but numerator goes to -110

Answer 6

no do nothing

Answer 7

if you do not get 0/0 you have no hope of finding a limit

Answer 8

plug in 121 for x and the numerator is not zero, but rather -110

Answer 9

you have to though, prof is all abt rationalizing the denom though>?

Answer 10

there is absolutely no point in it. really

Answer 11

pls explain? thanks!

Answer 12

if i want

\[lim_{x\rightarrow 1}\frac{x+2}{x-1}\]

Answer 13

i see that the denominator goes to 0, but the numerator does not!

Answer 14

gotcha. if I were to rationalize what would the equation be to rationalize ( want to check my rationalizing skills regardless)

Answer 15

so there is nothing more to do. i get no limit. just like in your example

Answer 16

you can do whatever you want, of course, but you would be better served practicing rationalizing the denominator if the problem was

\[lim_{x->121}\frac{x-121}{\sqrt{x}-11}\]

Answer 17

ok cool, so it is DNE

Answer 18

because in this case you would get 0/0 and so will have a hope of getting something as a limit

Answer 19

did you use sqrt(x) +11 to rationalize?

Answer 20

yes. assuming the problem is as written. i think the whole point of this problem is for you to check what you get before you start doing anything

Answer 21

is zero over zero considered DNE or 0?

Answer 22

neither.

Answer 23

hold on lets go slow

Answer 24

when I rationalize i get a different answer to you?

Answer 25

ok, sorry :-)

Answer 26

you want to take a limit of a fraction say. first you just try plugging in the number.
if you get out a number, say 3/2, then that is your answer.

if you get out say -110/0 or anything not 0 /0 there is no answer

if you get 0/0 you have more work to do. you do not write DNE or 0. you have to do more work to find the limit

Answer 27

I get (x-11)/(sqrt(x)-11) times (-sqrt(x)-11)/(-sqrt(x)-11)

Answer 28

you first have to factor before plugging in

Answer 29

step 1 is just plug in the number, because if you do not get 0/0 there is no need to continue

Answer 30

so in your problem since you got -110/0 stop right there and say DNE

Answer 31

now in the problem i sent you, you do get 0/0

Answer 32

so now there is more work to do. you need to "rationalize the denominator"

Answer 33

ok, understand thus far

Answer 34

multiply top and bottom by the conjugate of

\[\sqrt{x}-11\]
which is

\[\sqrt{x}+11\]

Answer 35

let me know what you get

Answer 36

ok, I used -sqrt(x)+11

Answer 37

first time round I used what you said

Answer 38

i get sqrt(x)-121 in the denom - therefore that is zero !

Answer 39

sorry sat, my connection is stalling

Answer 40

zero in the denom, whch means it is DNE

Answer 41

Thank you so much SAT!!!

Answer 42

hole on

Answer 43

are you doing the problem i sent you?

Answer 44

or a different one?

Answer 45

I was using the wrong equation to rationalize,

Answer 46

I see what I was doing incorrect and understand it now

Answer 47

*incorrectly

Answer 48

ok because if you rationalize the denominator you should be able to factor and cancel yes?

Answer 49

btw the answer to your next question is -1

Answer 50

haha, you are too good!

Answer 51

well it is really just
\[f(x)=-1\] if x < 4 and
\[f(x)=1\] if x > 4

Answer 52

\[\frac{x-121}{\sqrt{x}-11}=\frac{x-121}{\sqrt{x}-11}\times \frac{\sqrt{x}+11}{\sqrt{z}+11}=\frac{(x-121)(\sqrt{x}+11)}{x-121}=\sqrt{x}+11\]

Answer 53

=\[\sqrt{x}+11\] now replace x by 121 to get 22