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- anonymous

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- anonymous

@jim_thompson5910 they said u could help

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- anonymous

I think the answer does not Exist

- jim_thompson5910

using the limit laws, we can say
\[\Large \lim_{x\to 2}x^3 f(x) = (\lim_{x\to 2}x^3) * (\lim_{x\to 2}f(x))\]
\[\Large \lim_{x\to 2}x^3 f(x) = 2^3 * f(2)\]
\[\Large \lim_{x\to 2}x^3 f(x) = 8 * f(2)\]
\[\Large \lim_{x\to 2}x^3 f(x) = ???\]

- jim_thompson5910

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

- anonymous

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

- anonymous

at x->2

- jim_thompson5910

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

- jim_thompson5910

\[\Large \lim_{x\to 2}x^3 f(x) = (\lim_{x\to 2}x^3) * (\lim_{x\to 2}f(x))\]
\[\Large \lim_{x\to 2}x^3 f(x) = 2^3 * 2\]
\[\Large \lim_{x\to 2}x^3 f(x) = 8 * 2\]
\[\Large \lim_{x\to 2}x^3 f(x) = 16\]

- anonymous

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

- jim_thompson5910

sure go for it

- anonymous

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

- anonymous

im getting 8 as a result not sure

- jim_thompson5910

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

- jim_thompson5910

oh wait nvm

- anonymous

yes

- jim_thompson5910

that's correct, g(1) = 8

- jim_thompson5910

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

- anonymous

yay! Thank You so much for your help!

- jim_thompson5910

you're welcome

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