You can put this solution on YOUR website! lim
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.
