Answer:
0
Step-by-step explanation:
To solve this without L'Hopital's rule, you need to use this identity:
lim(x→0) (sin x / x) = 1
lim(x→0) (sin²x / x)
lim(x→0) (sin x / x) (sin x)
lim(x→0) (sin x / x) · lim(x→0) (sin x)
1 · 0
0
Alternatively, since plugging in x=0 gets 0/0, we can use L'Hopital's rule. Replace the numerator and denominator with their derivatives.
lim(x→0) (sin²x / x)
lim(x→0) (2 sin x cos x / 1)
0
