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(Solved): did i do this correctly ? Evaluate: \lim_(x-> \infty )(1-cosx)/(sinx) \lim_(x->0)(1-cos( ...
did i do this correctly ? Evaluate:
\lim_(x-> \infty )(1-cosx)/(sinx)
\lim_(x->0)(1-cos(x))=0
\lim_(x->0)(sin(x))=0
\lim_(x->0)((1-cos(x))/(sin(x)))=(((1-cos(x))x)/(sin(x)*x))=((1-cos(x))/(x)*(x)/(sin(x)))
\lim_(x->0)((1-cos(x))/(x))*\lim_(x->0)((x)/(sin(x)))=0*1=0(?)Evaluate:
\lim_(x->4)(\sqrt(x)-2)/(x-4)
\lim_(x->4)(\sqrt(x)-2)=0
\lim_(x->4)(x-4)=0
\lim_(x->4)((\sqrt(x)-2)/((\sqrt(x)-2)(\sqrt(x) 2)))=\lim_(x->4)((1)/(\sqrt(x) 2))=(1)/(\sqrt(4) 2)=(1)/(4)(!)