Question

I just need someone to check my answer! I'll fan and medal

Use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 6 as x approaches 6 from the left.

Answer 1

Choices:
-∞ ; x = 6
-∞ ; x = -6
∞ ; x = -6
1 ; no vertical asymptotes

Answer 2

I can't choose between A and C

Answer 3

@phi @PartyShotz2409 @paki

Answer 4

Approaching 6 "from the left" means "left of 6" i.e. from the side of 5

\[ \lim_{x\rightarrow 6^-} \frac{1}{x-6} \]

Answer 5

if x is (for example) we get 1/(5-6) = 1/-1 = -1
as long as x is smaller than 6 we will get a minus number, right ?
example: 5.9999 - 6 = -0.0001
and 1/ (-0.0001) = - 10000 (it looks like we are *very* negative as we get closer to 6)

Answer 6

Ohh okay

Answer 7

"limit" means we get close to x=6 (but never are allowed to reach it)
it should be obvious the asympote is x=6 (and not x= -6, because we are not anywhere near x= -6)

Answer 8

That makes sense! So it is A?

Answer 9

yes

Answer 10

Thanks! Can you help with a couple more pleaseee?

Answer 11

one more

Answer 12

Okay fair enough

Answer 13

Find an equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±11).