#### 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)[(3x-(3x)^2/2+(3x)^3/3-.........)/(5x)]`

=`Lim_(x→0)[3/5-(9x)/10+9/5x^2..........]`

=`3/5`

∵ f is continuous at x=0

∴ `Lim_(x→0) f(x)=f(0)⇒ k=3/5`

Is there an error in this question or solution?

#### APPEARS IN

Solution Find K, If F(X) = Log ( 1 + 3 X ) 5 X for X ≠ 0 = K for X = 0 is Continuous at X = 0. Concept: Continuous Function of Point.