Question 847230
lim      {{{(x*tan(x))/(1-cos(x))}}}
x->0 

using l'hopital's rule:

derivative of numerator [use product rule] =  x *sec^2(x) + tan(x)

derivative of denominator =  sin(x)

plugging in 0 to numerator =  0

plugging in 0 to denominator = 0

Use L'hopital's rule again

derivative of new numerator [use product rule] = (2x*tan(x)+1)sec^2(x) + x*sec^2(x) +  tan(X) =  2(xtan(x) + 1)*sec^2(x)

derivative of new denominator = cos(x)

plugging in 0 into numerator =   2 * 1 = 2

plugging in 0 into denominator = 1

So the limit is 2/1 =  2.