Question #15ada

1 Answer
NickTheTurtle
Feb 13, 2018

#lim_(x->0)x/sqrt(1-cos(x))=sqrt(2)#

Explanation:

#\ \ \ \ \ \ lim_(x->0)x/sqrt(1-cos(x))#
#=lim_(x->0)x/sqrt(1-cos(x))*sqrt(1+cos(x))/sqrt(1+cos(x))#
#=lim_(x->0)(xsqrt(1+cos(x)))/sqrt(1-cos^2(x))#
#=lim_(x->0)(xsqrt(1+cos(x)))/sin(x)#
#=lim_(x->0)x/sin(x)sqrt(1+cos(x))#
#=lim_(x->0)x/sin(x)*lim_(x->0)sqrt(1+cos(x))#
#=1*sqrt(2)#
#=sqrt(2)#

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