Question

\[\[\lim_{x \rightarrow 6}(\frac{ \sqrt[5]{x^2-4}-2 }{ x-6 })\]\]

Answer 1

Evaluate the following limits

Answer 2

@AravindG

Answer 3

HELPP Q~Q

Answer 4

that looks scary

Answer 5

@nincompoop

Answer 6

how is that a logarithmic problem?

Answer 7

in order to solve it im pretty sure u have to log it first

Answer 8

no

Answer 9

so you dont natural log it?

Answer 10

it is up to you, this is where all of your algebra knowledge come into play

Answer 11

your goal is to achieve a non-zero denominator

Answer 12

i do remember you can switch lim and ln around and put lim on outside and ln on inside. i did that and i dont know how to follow up with it. :( im trying to achieve the non zero denominator...

Answer 13

it doesn't matter how crazy your numerator is. your issue will be your denominator being zero

Answer 14

try whatever you're talking about and we'll see how is that going to pan out

Answer 15

\[\lim_{x \rightarrow 6}(\ln (\sqrt[5]{x^2-4}-2) - \ln (x-6))\]

Answer 16

is where i got to.... after using my method

Answer 17

i dont know where to go after that

Answer 18

can you rewrite your question because it is not displaying correctly

Answer 19

This limit problem is a perfect candidate for L'Hopital's Rule.

Answer 20

That explains why I don't get it... our teacher hasn't covered this part yet. Thanks!

Answer 21

how come the problem is not rendering correctly on my screen...?

Answer 22

\[\lim_{x \rightarrow 6}(\frac{ \sqrt[5]{x^2-4}-2 }{ x-6 })\]

Answer 23

^thats the problem if u still want to see it

Answer 24

show the hospital's way (laughing out loud) @Easyaspi314

Answer 25

I am happy to learn this if it didn't give us a DNE

Answer 26

limit DNE

Answer 27

Sure...The derivative of the denominator is just 1...so we just need the derivative of numerator...and that is (using chain rule), (2x/5)(x^2 - 4)^(-4/5)......as x----> 6, that's just 3/20.

Answer 28

And it's quite evident from the graph...that it approaches .15 or 3/20.

Answer 29

I graphed it and it gave me asymptotes

Answer 30

Sorry, then you didn't enter it correctly. Be careful as you need parenthesis..plenty of them.

I showed a pretty accurate graph of the function.

Answer 31

Enter the function as:

((x^2 - 4)^(.2) - 2)/(x-6)

Answer 32

That should you give the correct graph.

Answer 33

nvm I did a typo I put -2 instead of -4

Answer 34

ok.

Answer 35

it's why I asked you to do l'hospital earlier because the graph I had would not have any limit

Answer 36

it is not rendering properly on my screen

Answer 37

I dont see that on my screen. I see it nicely "typeset".

Answer 38

thanks for your help

Answer 39

no problem. take care.