COMEDK · Maths · 16. Limits
Find the value of \(\lim _{h \rightarrow 0} \dfrac{(a+h)^2 \sin (a+h)-a^2 \sin a}{h}\)
- A \(1\)
- B \(-a^2 \sin a\)
- C \(0\)
- D \(a^2 \cos a+2 a \sin a\)
Answer & Solution
Correct Answer
(D) \(a^2 \cos a+2 a \sin a\)
Step-by-step Solution
Detailed explanation
The given limit is of the form \(f'(a) = \lim_{h \to 0} \dfrac{f(a+h) - f(a)}{h}\) where \(f(x) = x^2 \sin x\) Differentiating using product rule: \(f'(x) = 2x \sin x + x^2 \cos x\) At \(x = a\): \(f'(a) = 2a \sin a + a^2 \cos a\)
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