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Honour

  • 3 years ago

If possible, choose k so that the following function is continuous on any interval (equation in post).

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  1. Honour
    • 3 years ago
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    \[f(x)=\left[\begin{matrix}kcos(x), & x \le0 \\ 10e^{x}-k,&0< x \end{matrix}\right]\]

  2. Honour
    • 3 years ago
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    @rebeccaskell94

  3. rebeccaskell94
    • 3 years ago
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    I haven't passed 4th grade math yet.

  4. Honour
    • 3 years ago
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    Oh that's ok then (= thanks anyhow

  5. hartnn
    • 3 years ago
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    do you know the basics of continuity ?

  6. Honour
    • 3 years ago
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    that the line must contiously go and still be a function (one to one) =P if that's what you mean

  7. hartnn
    • 3 years ago
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    i meant, if f(x) is continuous, at x=0, \[\lim \limits{x \rightarrow 0^-} f(x)=\lim \limits{x \rightarrow 0^+f(x)}\]

  8. hartnn
    • 3 years ago
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    do you you something like that ^ ?

  9. Honour
    • 3 years ago
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    |dw:1359178608600:dw|

  10. hartnn
    • 3 years ago
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    for x->0- , since x<0, select k cos x and put x=0 for x->0+ , since x>0, select 10e^x-k and put x=0

  11. Honour
    • 3 years ago
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    Honestly that is all I know

  12. Honour
    • 3 years ago
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    uhh...

  13. hartnn
    • 3 years ago
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    when x->0-, lim kcos x = k cos 0 = k when x->0+, lim 10e^x-k = 10e^0-k =10- k for continuity k=10-k can you find k from here ?

  14. hartnn
    • 3 years ago
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    just add k to both sides.

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