Question

Solve the limit:
x/(sqrt(x^2-9))
as x approaches -3-
What I'm confused about is the small minus after the 3.

Answer 1

that just means from the left

Answer 2

It means it is approaching from the left :)

Answer 3

So, would I solve it normally then?

Answer 4

we know it goes to -infinity because its negative for values to the left of -3

Answer 5

This is quite a handy little website to understand right and left limits
http://calculus.nipissingu.ca/tutorials/limits.html

Answer 6

like if you put in x=-3.1 you have negative on top and positive on bottom, so it goes to -infinity now infinity...

Answer 7

@pokemonmaster96 understand?

Answer 8

I guess you actually didn't need to do all that, lol
you have -3/0 so we know it diverges, now use the argument above to know it goes to -infinity

Answer 9

Does this mean the limit doesn't exist?

Answer 10

correct

Answer 11

there are not great shortcut rules to show left/right handed limits, you sort of just have to use what you know about how things behave. unless you want to prove it epsilon-delta style...and you dont

Answer 12

Okay, thank you. :)

Answer 13

np
for more clarity think of the example limit as x goes to 0 of 1/x
this diverges, and when we approach 0 from the left its negative (1/-.0000001) and when we approach 0 from the right its positive (1/.0000000001)

Answer 14

ok im done:)