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



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\[f(x)=\left[\begin{matrix}kcos(x), & x \le0 \\ 10e^{x}k,&0< x \end{matrix}\right]\]

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@rebeccaskell94

rebeccaskell94
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I haven't passed 4th grade math yet.

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Oh that's ok then (= thanks anyhow

hartnn
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do you know the basics of continuity ?

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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

hartnn
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i meant, if f(x) is continuous, at x=0,
\[\lim \limits{x \rightarrow 0^} f(x)=\lim \limits{x \rightarrow 0^+f(x)}\]

hartnn
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do you you something like that ^ ?

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dw:1359178608600:dw

hartnn
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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^xk and put x=0

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Honestly that is all I know

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uhh...

hartnn
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when x>0, lim kcos x = k cos 0 = k
when x>0+, lim 10e^xk = 10e^0k =10 k
for continuity
k=10k
can you find k from here ?

hartnn
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just add k to both sides.