lim x → 0 sin 2 4 x 2 x 4

limx→0sin2 4x2x4 = limx→0sin4x2x2×sin4x2x2= limx→0sin4x24x2×4×sin4x24x2×4= 4×4 ∵limx→0sin xx=1= 16

$\lim_{x \to 0} \frac{\sin^{2} 4 x^{2}}{x^{4}}$

\lim_{x \to 0} [\frac{\sin^{2} 4 x^{2}}{x^{4}}]

= \lim_{x \to 0} [\frac{\sin (4 x^{2})}{x^{2}} \times \frac{\sin (4 x^{2})}{x^{2}}] = \lim_{x \to 0} [\frac{\sin (4 x^{2})}{4 x^{2}} \times 4 \times \frac{\sin (4 x^{2})}{4 x^{2}} \times 4] = 4 \times 4 [∵ \lim_{x \to 0} \frac{\sin x}{x} = 1] = 16