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  • Let  <img alt="\mathrm{f(x)=\frac{\sin 4 \pi[x]}{1+[x]^2}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bf%28x%29%3D%5Cfrac%7B%5Csin%204%20%5Cpi%5Bx%5D%7D%7B1&plus

Let  \mathrm{f(x)=\frac{\sin 4 \pi[x]}{1+[x]^2}}  , where [x] is the greatest integer less than or equal to x, then

Option: 1

f(x) is not differentiable at some points
 


Option: 2

f(x) exists but is different from zero
 


Option: 3

f(x)=0 for all x


Option: 4

f(x)=0 but f is not a constant function.


Answers (1)

best_answer

We have 

\mathrm{f(x)=\frac{\sin 4 \pi[x]}{1+[x]^2}=0 ~for ~all ~x \quad[\because 4 \pi[x]~is ~a~ multiple~ of ~\pi]}

\mathrm{\Rightarrow f^{\prime}(x)=0~for ~all ~x}

Posted by

Devendra Khairwa

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