InterviewSolution
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InterviewSolution
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Evaluate : \(\lim\limits_{h \to 0}\frac{(a+h)^2sin(a+h)-a^2sin\,a}{h}\) |
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Answer» \( \lim\limits_{h \to 0}\frac{(a+h)^2sin(a+h)-a^2sin\,a}{h}\) \( \lim\limits_{h \to 0}\frac{(a^2+h^2+2ah)[sin\,a\,cosh+cosasinh)-a^2sin\,a}{h}\) \( \lim\limits_{h \to 0}[\frac{a^2\,sin\,a(cosh-1)}{h}\) \(\frac{a^2\,sin\,a\,sin\,h}{h}+(h+2a)(sin\,a\,cosh+cos\,a\,sin\,h)]\) = \( \lim\limits_{h \to 0}[\frac{a^2\,sin\,a(-2sin^2\frac{h}{2})}{h}.\frac{h}{2}]\) \(+ \lim\limits_{h \to 0}\frac{a^2\,cos\,a\,sin\,h}{h}+\lim\limits_{h \to 0}(h+2a)sin(a+h)\) = \(-a^2\,sin\,a.1^2.0+a^2\,cos\,a.1+2a\,sin\,a\) = \(a^2\,cosa+2a\,sin\,a.\) |
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