What is \lim_{h\rightarrow0}\frac{\sin^{2}(x+h)-\sin^{2}x}{h} equal to ?
- A. \sin^{2}x
- B. \cos^{2}x
- C. \sin 2x ✓
- D. \cos 2x
Correct Answer: C. \sin 2x
Explanation
By definition, this limit represents the derivative of the function f(x) = \sin^2 x with respect to x. Differentiating \sin^2 x using the chain rule gives 2\sin x \cos x, which simplifies to \sin 2x.
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