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  • <img alt="\mathrm{f(x)=\frac{\sin \pi[\pi-x]}{3+[x]}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bf%28x%29%3D%5Cfrac%7B%5Csin%20%5Cpi%5B%5Cpi-x%5D%7D%7B3&plus;%5Bx%5D%7D%7

\mathrm{f(x)=\frac{\sin \pi[\pi-x]}{3+[x]}}  is, (where [-] represents greatest integer function) 

Option: 1

differentiable for all \mathrm{x \in R}
 


Option: 2

continuous and differentiable for all x \in R
 


Option: 3

continuous and differentiable everywhere except forx \in[-3,-2)
 


Option: 4

f(x) is twice differentiable for all x \in R


Answers (1)

best_answer

\mathrm{ f(x)=\left\{\begin{array}{lll} 0 & ; & x \in R-[-3,-2) \\ N . D . & ; & x \in[-3,-2) \end{array}\right. }

\mathrm{\therefore \quad f(x)}  is continuous and differentiable for all \mathrm{x \in R \sim[-3,-2).}

Posted by

Deependra Verma

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