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anonymous

  • one year ago

help please ! to two decimal places, find the value of k that will make the function f(x) continuous everywhere.

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  1. anonymous
    • one year ago
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    |dw:1434088494322:dw|

  2. freckles
    • one year ago
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    evaluate both the left and right limit of x=4

  3. freckles
    • one year ago
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    \[\lim_{x \rightarrow 4^-}f(x)=? \\ \lim_{x \rightarrow 4^+}f(x)=?\]

  4. freckles
    • one year ago
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    oops -4

  5. anonymous
    • one year ago
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    my choices are: 11.00 -2.47 -0.47 none of these

  6. freckles
    • one year ago
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    ok can you evaluate both: \[\lim_{x \rightarrow -4^-}f(x)=? \\ \lim_{x \rightarrow -4^+}f(x)=?\]

  7. freckles
    • one year ago
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    hint ^- means look to the left (which is the left function of x=-4 and use it to plug in -4 into) hint ^+ means look to the right (which is the right function of x=-4 and use it to plug in -4 into) both the left and right limit need to be equal so that you can have the actual limit at x=-4 exist

  8. anonymous
    • one year ago
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    o.o im lost lol

  9. freckles
    • one year ago
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    |dw:1434077995749:dw|

  10. freckles
    • one year ago
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    |dw:1434078038396:dw|

  11. anonymous
    • one year ago
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    is it A?

  12. freckles
    • one year ago
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    I don't know. Haven't done the problem.

  13. freckles
    • one year ago
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    would you know how to evaluate: \[\lim_{x \rightarrow -4}(3x+k) \text{ or } \lim_{x \rightarrow -4}(kx^2-5)\]

  14. anonymous
    • one year ago
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    no. o.o

  15. freckles
    • one year ago
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    Both functions are continuous at x=-4 why don't you evaluate the limits by replacing x with -4?

  16. freckles
    • one year ago
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    and you want both (left and right limits of x=-4) sides to be equal so you have \[3(-4)+k=k(-4)^2-5\]

  17. freckles
    • one year ago
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    can you solve linear equations?

  18. anonymous
    • one year ago
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    Do you have to take a limit here? Can you just substitute -4 for x and set the two parts equal to each other?

  19. freckles
    • one year ago
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    one of the things we need for continuity at x=-4 is: \[\lim_{x \rightarrow -4}f(x)=L\] we get to have this if : \[\lim_{x \rightarrow -4^{-} }f(x)=\lim_{x \rightarrow -4^{+}}f(x)=L\] so formally the answer is yes to that question

  20. freckles
    • one year ago
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    to the limit one

  21. freckles
    • one year ago
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    and informally ( I would say) yes to the second question

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