limit (cos3x)^5/x as x approaches 0?

Question

L'hospital's rule
derivatives?---I don't understand math at all

Answer 1

L'Hospita;'s rule shall not apply here as it is non zero/zero form

it applies for form 0/0 or infinite.infinite

limit f(x)/g(x) when it is of above form is lim f'(x)/g'(x)

for example as x->o lim sin x/ x is of the form 0/0
= lim x->0 d/dx(sin x)/d/dx(x)
= cos x/ 1= cos x = 1 when x->0

for your case it is 1/0 or infinite (no l'Hospital's rule)

Answer 2

(cos 0)^5/0 = 1/0, so this function must diverge to infinity as x→0. Furthermore, the sign of the infinity differs between the left and right-hand sides (negative on the left and positive on the right), so this function has no limit at 0.