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Question Number 184792 by Spillover last updated on 11/Jan/23
Evaluatelimx→0tanx−sinxsin3x
Commented by MJS_new last updated on 11/Jan/23
12
Commented by Spillover last updated on 11/Jan/23
thankyou
Answered by aba last updated on 12/Jan/23
letx=2ulimx→0tan(x)−sin(x)sin3(x)=limu→0tan(2u)−sin(2u)sin3(2u)=limu→0sin(2u)(1cos(2u)−1)sin3(2u)=limu→01cos(2u)−1sin2(2u)=limu→01−cos(2u)cos(2u)(1−cos2(u))=limu→01cos(2u)(1+cos(2u))=12
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