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  • For the function <img alt="f(x)=\lim _{n \rightarrow \infty} \frac{1}{2+n \sin ^2(\pi x)}" src="https://entrancecorner.oncodecogs.com/gif.latex?f%28x%29%3D%5Clim%20_%7Bn%20%5Crightarrow%20%5Cinfty%

For the function f(x)=\lim _{n \rightarrow \infty} \frac{1}{2+n \sin ^2(\pi x)}, which of the following holds?
 

Option: 1

The range of f is a singleton set
 


Option: 2

f is continuous on R
 


Option: 3

f is discontinuous for all x \in I
 


Option: 4

 None of these


Answers (1)

best_answer

 

\mathrm{ : f(x)=\left\{\begin{array}{cl}1 / 2, & \text { if } x \in I \\ 0, & \text { if } x \notin I\end{array}\right. }
\mathrm{as\, \, \sin \pi x=0 \forall x \in I \Rightarrow \quad f \, is \, \, discontinuous \, \, for\, \, all \, \, x \, \, \in I }

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Shailly goel

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