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Question 9.14

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TZ
leumasicOfficial

3 months ago

We have

f(0)=limh0f(h)f(0)h=limh0f(h)h=0.f'(0)=\lim_{h\to 0}\frac{f(h)-f(0)}{h}=\lim_{h\to 0}\frac{f(h)}{h}=0.

Since

f(h)h={0,if h is rational,h2h=h,otherwise,\frac{f(h)}{h}=\begin{cases} 0, & \text{if } h \text{ is rational},\\ \frac{h^2}{h}=h, & \text{otherwise}, \end{cases}

the limit is 00.

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Q 9.14

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Q 9.14