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Let $y(x)=a x^{n}$ and $\delta y$ denote small change in $y$. What is limit
of $\frac{\delta y}{\delta x}$ as $\delta x \rightarrow 0 ?$
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of $\frac{\delta y}{\delta x}$ as $\delta x \rightarrow 0 ?$
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Verified Answer
The correct answer is:
0
We know $\lim _{\delta x \rightarrow 0} \frac{\delta y}{\delta x}=\left(\frac{d y}{d x}\right)_{\text {at } x=0}$
$\quad=\frac{d}{d x}\left(a x^{n}\right)_{\text {at } x=0}=\left(\operatorname{an} x^{n-1}\right)_{\mathrm{at} x=0}=0$
$\quad=\frac{d}{d x}\left(a x^{n}\right)_{\text {at } x=0}=\left(\operatorname{an} x^{n-1}\right)_{\mathrm{at} x=0}=0$
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