7 (b) lim(x→0) (sin x² / sin² x)
7 (b) lim(x→0) (sin x² / sin² x)
Answer
# Explanation:
## Step1: Use equivalent - infinitesimals
When \(x\to0\), \(\sin u\sim u\). So when \(x\to0\), \(\sin x^{2}\sim x^{2}\) and \(\sin x\sim x\).
## Step2: Substitute equivalent - infinitesimals
\(\lim_{x\rightarrow0}\frac{\sin x^{2}}{\sin^{2}x}=\lim_{x\rightarrow0}\frac{x^{2}}{x^{2}}\)
# Answer:
1