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  • Let <img alt="\mathrm{f}(\mathrm{x})=\left\{\begin{array}{cc} {[\mathrm{x}] / \tan \m

Let \mathrm{f}(\mathrm{x})=\left\{\begin{array}{cc} {[\mathrm{x}] / \tan \mathrm{x},} & 0<\mathrm{x}<\pi, \quad \mathrm{x} \neq \pi / 2 \\ \mathrm{a}, & \mathrm{x}=\pi / 2 \end{array}\right. . If f is continuous in (0, π), then a = 

 

Option: 1

0


Option: 2

\infty


Option: 3

-\infty


Option: 4

does not exist 

 


Answers (1)

best_answer

In the nbd of π/2, [x] = 1, and tan x can be made as large as we like, in the modulus value, in the deleted nbd of π/2.Hence a = \lim _{x \rightarrow \frac{\pi}{2}} f(x)=0

 

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