Hello! I need some advices for Calculus homework. Any help is appreciated!

1 - Why this limit doesn't exist?



2 - c, L ∈ R

c = ?
L = ?

Offering 100fg for each question (only the most detailed and clear explanation will get the payment)
I used this website to write the equations: https://www.codecogs.com/latex/eqneditor.php

For the first one, if you approach 0 from the negative side (x < 0) then you will approach y = -1
if you approach from the positive side (x > 0) you will approach y = 1.
Because you are not getting the same value for both of these, there is no limit as x approaches 0.
Though there are limits as you approach from certain directions, if those two do not agree, then you do not have THE limit of that expression.

I have no idea what you're asking on the second question.

Thanks for the answer! I understood it, but how am I going to notice this when I'm in a test? (I new this particular one didn't exist because I saw the answer). Should I always draw the graph before calculating it? Are there any steps to follow?

And the second one had a mistake, sorry about that.

http://imgur.com/JUiH627

I have to find the values of L and c. L, c ∈ R

This post was edited by Ornitier on Mar 8 2015 03:28pm

since L is a real number and the denominator is 0, you want the numerator to equal 0 as well.

2x^3 + cx + c = 0

x = 1, so:
2 + c + c = 0
2 + 2c = 0
2c = -2
c = -1

now just evaluate the limit

Just write :

√ ( x^4 + x²) = √ ( x² ( x² + 1 )) = √(x²) . √(x² + 1 ) = |x| . √(x² + 1)

√(x² + 1) obviously tends to 1

|x| / x = 1 if x > 0, and = -1 if x < 0.

Ooh, I see it now! Thanks a lot!



Understood! Thank you for your help!

Everything was answered, so the thread may be closed or whatever.

I suggest graphing it, as well as trying to visualize it.
When you graph it and see that approaching 0 from different sides brings you to different values (in other words, there is a break in the curve/line/whatever) then there is no limit.
Like I said, you can have a limit from the right, and a limit from the left, but if they aren't the same, then you have no limit as you approach that value in general.
Good luck