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dainel40

  • 2 years ago

Find the limit of this look at the attached file

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  1. dainel40
    • 2 years ago
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  2. dainel40
    • 2 years ago
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  3. dainel40
    • 2 years ago
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    @jim_thompson5910 they said u could help

  4. dainel40
    • 2 years ago
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    I think the answer does not Exist

  5. jim_thompson5910
    • 2 years ago
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    using the limit laws, we can say \[\Large \lim_{x\to 2}x^3 f(x) = (\lim_{x\to 2}x^3) * (\lim_{x\to 2}f(x))\] \[\Large \lim_{x\to 2}x^3 f(x) = 2^3 * f(2)\] \[\Large \lim_{x\to 2}x^3 f(x) = 8 * f(2)\] \[\Large \lim_{x\to 2}x^3 f(x) = ???\]

  6. jim_thompson5910
    • 2 years ago
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    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

  7. dainel40
    • 2 years ago
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    but the graph has a hole and a solution thats where im confused

  8. dainel40
    • 2 years ago
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    at x->2

  9. jim_thompson5910
    • 2 years ago
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    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 \[\Large \lim_{x\to 2} f(x) = 2\]

  10. jim_thompson5910
    • 2 years ago
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    \[\Large \lim_{x\to 2}x^3 f(x) = (\lim_{x\to 2}x^3) * (\lim_{x\to 2}f(x))\] \[\Large \lim_{x\to 2}x^3 f(x) = 2^3 * 2\] \[\Large \lim_{x\to 2}x^3 f(x) = 8 * 2\] \[\Large \lim_{x\to 2}x^3 f(x) = 16\]

  11. dainel40
    • 2 years ago
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    oh... I see.. Thanks a lot! I have another question.. Could I ask you?

  12. jim_thompson5910
    • 2 years ago
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    sure go for it

  13. dainel40
    • 2 years ago
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    If f and g are continuous functions with f(1) = 5 and the following limit, find g(1).

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  14. dainel40
    • 2 years ago
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    im getting 8 as a result not sure

  15. jim_thompson5910
    • 2 years ago
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    this is a completely different problem right (with different functions f and g)?

  16. jim_thompson5910
    • 2 years ago
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    oh wait nvm

  17. dainel40
    • 2 years ago
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    yes

  18. jim_thompson5910
    • 2 years ago
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    that's correct, g(1) = 8

  19. jim_thompson5910
    • 2 years ago
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    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

  20. dainel40
    • 2 years ago
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    yay! Thank You so much for your help!

  21. jim_thompson5910
    • 2 years ago
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    you're welcome

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