Question

Find k, if f(x) =`log (1+3x)/(5x)` for x ≠ 0

                     = k                    for x = 0

is continuous at x = 0. 

Answer 1

`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`