lim x-0 xtan(8x)+ 2tan(8x)/(x^2+4x)

Answer 1

Using L'Hopital's Rule,

lim f/g = lim f'/g'

f = (x+2) tan(8x)
g = x^2 + 4x

f' = tan(8x) + 8(x+2)sec^2(8x)
g' = 2x + 4

f'(0) = 16
g'(0) = 4

lim = 16/4 = 4