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Find the limit of this look at the attached file

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@jim_thompson5910 they said u could help

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Other answers:

I think the answer does not Exist
using the limit laws, we can say \[\Large \lim_{x\to 2}x^3 f(x) = (\lim_{x\to 2}x^3) * (\lim_{x\to 2}f(x))\] \[\Large \lim_{x\to 2}x^3 f(x) = 2^3 * f(2)\] \[\Large \lim_{x\to 2}x^3 f(x) = 8 * f(2)\] \[\Large \lim_{x\to 2}x^3 f(x) = ???\]
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
but the graph has a hole and a solution thats where im confused
at x->2
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 \[\Large \lim_{x\to 2} f(x) = 2\]
\[\Large \lim_{x\to 2}x^3 f(x) = (\lim_{x\to 2}x^3) * (\lim_{x\to 2}f(x))\] \[\Large \lim_{x\to 2}x^3 f(x) = 2^3 * 2\] \[\Large \lim_{x\to 2}x^3 f(x) = 8 * 2\] \[\Large \lim_{x\to 2}x^3 f(x) = 16\]
oh... I see.. Thanks a lot! I have another question.. Could I ask you?
sure go for it
If f and g are continuous functions with f(1) = 5 and the following limit, find g(1).
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im getting 8 as a result not sure
this is a completely different problem right (with different functions f and g)?
oh wait nvm
that's correct, g(1) = 8
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
yay! Thank You so much for your help!
you're welcome

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