anonymous
  • anonymous
Find the limit of this look at the attached file
Mathematics
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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anonymous
  • anonymous
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anonymous
  • anonymous
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anonymous
  • anonymous
@jim_thompson5910 they said u could help

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anonymous
  • anonymous
I think the answer does not Exist
jim_thompson5910
  • 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
  • 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
  • anonymous
but the graph has a hole and a solution thats where im confused
anonymous
  • anonymous
at x->2
jim_thompson5910
  • 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
  • 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
  • anonymous
oh... I see.. Thanks a lot! I have another question.. Could I ask you?
jim_thompson5910
  • jim_thompson5910
sure go for it
anonymous
  • anonymous
If f and g are continuous functions with f(1) = 5 and the following limit, find g(1).
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anonymous
  • anonymous
im getting 8 as a result not sure
jim_thompson5910
  • jim_thompson5910
this is a completely different problem right (with different functions f and g)?
jim_thompson5910
  • jim_thompson5910
oh wait nvm
anonymous
  • anonymous
yes
jim_thompson5910
  • jim_thompson5910
that's correct, g(1) = 8
jim_thompson5910
  • 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
  • anonymous
yay! Thank You so much for your help!
jim_thompson5910
  • jim_thompson5910
you're welcome

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