Let and f 4 : R R be functions defined by
(i) ,
(ii) where the inverse trigonometric function t…

Question

Let  and f 4 : R  R be functions defined by
(i)  ,
(ii)  where the inverse trigonometric function tan -1 x assumes values in  ,
(iii) f 3 (x) = [sin(log e (x + 2))], where, for t  R, [t] denotes the greatest integer less than or equal to t,
(iv) 
List IList IIP. The function f1 is1. NOT continuous at x=0Q. The function f2 is2. continuous at x=0 and NOT differentiable at x=0R. The function f3 is4. differentiable at x=0 and its derivative is continuous at x=0
The correct option is :

CGP EDU Academic Team · Accepted Answer

The correct answer is D. (i) 
f 1 (x) is continuous at x = 0

(ii) 
 Not continuous
(iii) 
 continuous at x = 0

differentiable at x = 0
 is 0 in neighbourhood of x = 0
so  is continuous at x = 0
(iv) f4(x) is continuous at x = 0
 is also differentiable at x = 0
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List I	List II
P. The function f1 is	1. NOT continuous at x=0
Q. The function f2 is	2. continuous at x=0 and NOT differentiable at x=0
R. The function f3 is	4. differentiable at x=0 and its derivative is continuous at x=0

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