Question

Please check just to make sure my notation is right, the limit of 3x^2g(x) as x approaches 2=? Given that the limit of g(x) as x approaches 2=-6

Answer 1

So My notation is 3 on the outside as the limit of x^3g(x) as x approaches 2=3(-6)^3

Answer 2

@zepdrix

Answer 3

You applied one limit law,\[\large\rm \lim_{x\to a} c f(x)=c\lim_{x\to a} f(x)\]Bringing the constant outside, yes.
But you should apply your other limit law as well,
the one for dealing with a product,\[\large\rm \lim_{x\to a}f(x)g(x)=\lim_{x\to a}f(x)\cdot \lim_{x\to a}g(x)\]

Answer 4

Huh?

Answer 5

Ohhhhh yeah!!! Because x^3 and g(x) are being multiplied

Answer 6

\[\large\rm \lim_{x\to2} (3x^3)g(x)\quad=\quad \lim_{x\to2} (3x^3)\cdot \lim_{x\to2} g(x)\]Yes good good good :)

Answer 7

And then pull the 3 out after that.

Answer 8

Or before, since it's multiplication, the ordering of these rules won't matter.

Answer 9

Yeah! Ok!!!

Answer 10

Woah, is it exclamation day? +_+

Answer 11

So than it will be 3(2)^3(-6)

Answer 12

Yes haha

Answer 13

Yes

Answer 14

Woops, I mean YESSSS!!!!!!!!

Answer 15

XD

Answer 16

-144 and yay!!!!