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