Evaluating Limits Analytically: lim[x->0] tan^2(x)/x, etc
1) tan 2x / x lim x-->0 sin2x/[xcos2x] lim x-->0 =0/0 undefined use L'hopitals rule d/dx [sin2x] / d/dx[x cos2x] lim x-->0 2cos2x/[ -2xsin2x- cos2x] lim x-->0 = 2/[0-1] =-2 answer 2) cosxtanx/x lim x-->0 but tan x= sinx/cosx cosxsinx/[xcosx] lim x-->0 sin...