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f(x)={{:(3x-8, if x le 5),(2k, if x gt...

` f(x)={{:(3x-8, if x le 5),(2k, if x gt 5) :}` at `x = 5`

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We have, ` f(x)={{:(3x-8, if x le 5),(2k, if x gt 5) :}` at `x = 5`
Since , `f(x)` is continous at `x = 5`.
`:. LHL = RHL = f(5)`
Now, `LHL = underset(xrarr5^(-))(lim)(3x-8)=underset(hrarr0)(lim)[3(5-h)-8]`
`= underset(hrarr0)(lim)[15-3h-8]=7`
`RHL = underset(xrarr5^(+))(lim)2k = underset(hrarr0)(lim)2k=2k=7, [:' LHL = RHL]`
and ` f(5) = 3xx5-8 = 7`
`:. 2k = 7 rArr k = 7/2`
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