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Question
Find k, if f(x) =`log (1+3x)/(5x)` for x ≠ 0
= k for x = 0
is continuous at x = 0.
Solution
`Lim_(x→0)[log(1+3x)/(5x)]`
=`lim_(x->0) log (1 + 3x)/(5x)`
=`lim_(x->0) log (1 + 3x)/(5x) xx 3/5`
= `1 xx 3/5`
=`3/5`
∵ f is continuous at x=0
∴ `Lim_(x→0) f(x)=f(0)⇒ k=3/5`
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