How do I solve this limits question??

enter image source here

1 Answer
maganbhai P.
Mar 14, 2018

#4#

Explanation:

#L=lim_(x to0)(tan2x-sin2x)/x^3=lim_(x to0)((sin2x)/(cos2x)-sin2x)/x^3#
#L=lim_(x to0)(sin2x(1-cos2x))/(x^3(cos2x))#
#L=lim_(x to0)1/(cos2x)*lim_(x to0)(sin2x)/(2x)*2lim_(x to0)(1-cos2x)/x^2#
#L=1/1(1)*2lim_(x to0)(1-cos^2(2x))/(x^2(1+cos2x)#
#L=2*lim_(x to0)(1/(1+cos2x))lim_(x to0)(sin^2(2x))/x^2#
#L=2*1/(1+1)lim_(x to0)((sin2x)/(2x))^2*4#
#L=2(1/2)(1)^2*4#
#L=4#

Related questions
Impact of this question
344 views around the world
You can reuse this answer
Creative Commons License