Question

Find the limit of this look at the attached file

Answer 1

@jim_thompson5910 they said u could help

Answer 2

I think the answer does not Exist

Answer 3

using the limit laws, we can say


\[\Large \lim_{x\to 2}x^3 f(x) = (\lim_{x\to 2}x^3) * (\lim_{x\to 2}f(x))\]


\[\Large \lim_{x\to 2}x^3 f(x) = 2^3 * f(2)\]


\[\Large \lim_{x\to 2}x^3 f(x) = 8 * f(2)\]


\[\Large \lim_{x\to 2}x^3 f(x) = ???\]

Answer 4

to find f(2) you would either use a function or the graph

since you don't have the function, you'll have to use the graph

Answer 5

but the graph has a hole and a solution thats where im confused

Answer 6

at x->2

Answer 7

ok as x gets closer and closer to 2, the graph is approaching the point (2,2)

sure there is a hole here, but if you start on either side of x = 2 and approach it, you'll reach this hole

so that's why

\[\Large \lim_{x\to 2} f(x) = 2\]

Answer 8

\[\Large \lim_{x\to 2}x^3 f(x) = (\lim_{x\to 2}x^3) * (\lim_{x\to 2}f(x))\]

\[\Large \lim_{x\to 2}x^3 f(x) = 2^3 * 2\]

\[\Large \lim_{x\to 2}x^3 f(x) = 8 * 2\]

\[\Large \lim_{x\to 2}x^3 f(x) = 16\]

Answer 9

oh... I see.. Thanks a lot! I have another question.. Could I ask you?

Answer 10

sure go for it

Answer 11

If f and g are continuous functions with f(1) = 5 and the following limit, find g(1).

Answer 12

im getting 8 as a result not sure

Answer 13

this is a completely different problem right (with different functions f and g)?

Answer 14

oh wait nvm

Answer 15

yes

Answer 16

that's correct, g(1) = 8

Answer 17

you separate the limit up

plug in x = 1

then replace f(1) with 5 and g(1) with y

afterwards you solve for y to get y = 8

Answer 18

yay! Thank You so much for your help!

Answer 19

you're welcome