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To use standard trig formula on limits, lim x→0 (sin x )/( x ) = 1 let us multiply numerator and denominator by 4.
= lim x→0 ( sin 4x ) • ( 4 ) / ( 4 • x )
= lim x→0 ( 4 ) • ( sin 4x )/ ( 4x ). ( taking constant 4 outside the limit )
= 4 lim x→0 ( sin 4x )/( 4x )
= 4 • 1 = 4
∴ lim x→0 ( sin 4x )/ ( x ) = 4
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