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  • Let <img alt="f(x)=\left [ \cos x+\sin \, x \right ],0<x<2\pi," src="https://learn.careers360.com/latex-image/?f%28x%29%3D%5Cleft%20%5B%20%5Ccos%20x&plus;%5Csin%20%5C%2C%20x%20%5Crig

Let f(x)=\left [ \cos x+\sin \, x \right ],0<x<2\pi,  where \left [ \cdot \right ] denotes G.I.F. The number of points of discontinity of f(x)  is -

 

Option: 1 6

Option: 2 5

Option: 3 4

Option: 4 3

Answers (1)

best_answer

 

Discontinuity -

The point where the graph of the function breaks is called the point of discontinuity.

-

 

 

Discontinuity -

A function is said to be discontinuous at a point a if there is a break in the graph of the function at x = a.

\lim_{x\rightarrow a^{-}}\:f(x)=\lim_{x\rightarrow a^{+}}\:f(x)=\lim_{x\rightarrow a}\:f(x)

if any one of the conditions is false the function will be discontinuous at x = a.

-

 

 

f(x)=\left [ \sqrt{2} \sin \left ( x+\frac{\pi}{4} \right )\right ]

discontinuity may arise at the points where

\sin \left ( x+\frac{\pi}{4} \right )=\frac{1}{\sqrt{2}},\sin\left ( x+\frac{\pi}{4} \right )=-\frac{1}{\sqrt{2}}

and  \sin \left ( x+\frac{\pi}{4} \right )=0

x = π/2 ,3π/4 , π, 3π/2 , 7π/4 so five point

Posted by

manish painkra

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