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Calculus homework studying for the test: Find K such that

  1. Apr 6, 2005 #1
    Calculus homework studying for the test: Find K such that this is continious

    [tex]f(x)=\left\{\begin{array}{cc}k&\mbox{ if }x=0\\2+\frac{Sin(x)}{x} &\mbox{ if }x\neq 0\end{array}\right[/tex]

    i have no clue how to find such a k that this is continious
     
    Last edited: Apr 7, 2005
  2. jcsd
  3. Apr 6, 2005 #2
    well, from your question I see no reason why I can't choose any [itex]k[/itex] that I like. Are you sure that's all there is to it?

    Perhaps you are trying to make [itex]f(x)[/itex] continuous?
     
    Last edited: Apr 6, 2005
  4. Apr 6, 2005 #3

    dextercioby

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    U didn't say what the problem wa about.I assume it required that the brach function would be continuous on R...Which means point "x=0",too.

    What's the condition for an univariable function defined on a domain [itex] \matcal{D}\subseteq \mathbb{R} [/itex] to be continuous in a point [itex] x \in \mathcal{D} [/itex]...?


    Daniel.
     
  5. Apr 6, 2005 #4
    Thats all the question says "find k such that this is continious"
     
    Last edited: Apr 7, 2005
  6. Apr 6, 2005 #5

    dextercioby

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    Then the aswer is [itex] k\in \mathbb{R} [/itex],which means an arbitrary #...

    Daniel.
     
  7. Apr 7, 2005 #6
    perhaps you should elaborate on the "blah blah," verbatim if possible. I find it highly doubtful that that is what it was asking for in a calculus course.
     
  8. Apr 7, 2005 #7

    xanthym

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    Well, IF the objective is to find "k" such that "f(x)" is continuous, what "k" would satisfy that condition??

    HINTS #1 & #2:

    [tex] 1: \ \ \ \ \lim_{x \longrightarrow 0} \, f(x) \ = \ f(0) [/tex]

    [tex] 2: \ \ \ \ \lim_{x \longrightarrow 0} \, \left (2 \ + \ \frac{\sin(x)}{x} \right ) \ = \ \color{red} \mathbf{???} [/tex]


    ~~
     
    Last edited: Apr 7, 2005
  9. Apr 7, 2005 #8

    saltydog

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    Well first like this:

    [tex]f(x)=\left\{\begin{array}{cc}k,&\mbox{ if }x=0\\2+\frac{Sin(x)}{x}, &\mbox{ if }x\neq 0\end{array}\right[/tex]

    Not too hard, check out the syntax in the editor.

    Then just do what Xanthym said to assure continuity.
     
  10. Apr 7, 2005 #9

    dextercioby

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    Maybe the function needs to be differentiable...:wink:

    Daniel.
     
  11. Apr 7, 2005 #10
    the problem is exactly like salty dog wrote it.
    and it says
    "Find K such that this is continious"
     
  12. Apr 7, 2005 #11
    [tex] 2: \ \ \ \ \lim_{x \longrightarrow 0} \, \left (2 \ + \ \frac{\sin(x)}{x} \right ) \ = \ \color{red} \mathbf{2?} [/tex]


     
  13. Apr 7, 2005 #12

    dextercioby

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    Incorrect.Check that "sin" limit again.

    Then u can get conclude what K needs to be...

    Daniel.
     
  14. Apr 7, 2005 #13
    the limit = 0, so K must be 0?
     
  15. Apr 7, 2005 #14
    lim {x->0} sin x/x = 1.
     
  16. Apr 7, 2005 #15
    so k must be 3 ?
     
  17. Apr 7, 2005 #16
    Deleting your previous post and then reposting exactly the same thing is a rather cunning way to get an answer :wink:

    Anyways, yes, that's fine.
     
  18. Apr 7, 2005 #17
    Correct. If you are unsure why [tex] \ \ \ \ \lim_{x \longrightarrow 0} \, \left (2 \ + \ \frac{\sin(x)}{x} \right ) \ = \ \ \mathbf{1} [/tex] you might have a look at the Taylor expansion of [tex] sin(x) [/tex] .
     
  19. Apr 7, 2005 #18
    You mean [itex]3[/itex] :smile:.
     
  20. Apr 7, 2005 #19

    dextercioby

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    We have a thread on the "sinc" limit.It has some good posts.

    Daniel.
     
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