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  • The right hand derivative of <img alt="f(x)=[x] \tan \pi x \: \text{at}\; x=7" src="https://entrancecorner.oncodecogs.com/gif.latex?f%28x%29%3D%5Bx%5D%20%5Ctan%20%5Cpi%20x%20%5C%3A%20%5Ctext%7Bat%7

The right hand derivative of f(x)=[x] \tan \pi x \: \text{at}\; x=7 is (where [.] denotes the greatest integer function)

Option: 1

0


Option: 2

7\pi


Option: 3

-7\pi


Option: 4

none of these 


Answers (1)

best_answer

\begin{aligned} f^{\prime}\left(7^{+}\right) & =\lim _{h \rightarrow 0} \frac{f(7+h)-f(7)}{h} \\ \\& =\lim _{h \rightarrow 0} \frac{[7+h] \tan \pi(7+h)-[7] \tan 7 \pi}{h} \\ \\& =\lim _{h \rightarrow 0} \frac{7 \tan \pi(7+h)}{h} \\ \\& =7 \pi \lim _{h \rightarrow 0} \frac{\tan \pi h}{\pi h} \\ \\& =7 \pi \end{aligned}

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Divya Prakash Singh

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