Evaluate lim(x tends to zero) x³cotx/1-cosx?

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Answer 1 · 2018-07-10T17:01:33

#2#

Writing your term in the form

#(x^3cos(x))/(sin(x)(1-cos(x))#

multiplying numerato and denominator by

#1+cos(x)#

we get

#(x^3cos(x)(1+cos(x)))/(sin(x)(1-cos^2(x))#
note that #1-cos^2(x)=sin^2(x)#

we get

#(cos(x)(1+cos(x)))/((sin(x)/x)^3)#
note that

#lim_(x to 0)sin(x)/x=1#

so we get

#(1*(1+1))/1=2#

as the searched Limit.