Q7 of 96 Page 16

Examine if the Rolle’s theorem applies to anyone of the following functions:

f(x) = [x] for xϵ[ – 2,2]

Given function is:


⇒ f(x) = [x] for xϵ[ – 2,2]


Let us check the continuity of the function ‘f’.


Here in the interval xϵ[ – 2,1], the function has to be Right continuous at x = 2 and left continuous at x = 2.


Right Hand Limit:


⇒


⇒ where h>0.


⇒


⇒ ......(1)


Left Hand Limit:


⇒


⇒ , where h>0


⇒


⇒ ......(2)


From (1) and (2), we can see that the limits are not the same so, the function is not continuous in the interval [ – 2,2].


∴ Rolle’s theorem is not applicable for the function f in the interval [ – 2,2].


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