Question

lim xtends to0 log(1+6x)/tan3x .Evaluate

Answer 1

Lim( x→0) { log( 1+ 6x)/tan3x

we know,
Lim( x→0) tanx/x = 1
and
Lim(x→0) log( 1 + x)/x = 1
use this here ,

Lim( x→0) { log( 1 + 6x)/6x ×6x}/tan3x/3x×3x

Lim(x→0)[ {log(1 + 6x)/6x}( 6x)/{tan3x/3x}(3x)

Lim(x→0)(6x/3x) = 2