Let f ( x ) = x | x | . The set of points where f ( x ) is twice differentiable is :

f ( x ) = min { sin x , cos x } i n 0 , π 4 then f ‘ ( 0 ) =

If f ( x ) = a | sin x | + b e | x | + c | x | 3 and if f ( x ) is differentiable at x = 0 , then

The function f ( x ) = max { 1 − x , 1 + x , 2 } , x ∈ ( − ∞ , ∞ ) is

The function f ( x ) = ( x − 1 ) | x − 1 | + sin ( | x | ) is

If f ( x + y ) − f ( x ) − f ( y ) = | x | y + x y 2 ∀ x , y ∈ R and f ′ ( 0 ) = 0 then

If f ( x ) = − 3 x + 2 , x < 1 1 2 x 2 + 7 , x ≥ 1 , then which of the following is not true

Let f ( x ) = x 1 + 2 1 / x , if x ≠ 0 0 if x = 0 then f 1 0 − =

If f ( x ) = | x − 1 | − [ x ] (Where [ X ] is greatest integer less than or equal to x ) then

The number of points of discontinuity of f ( x ) = Lt n ∞ x 2 n − 1 x 2 n + 1 is

If f ( x ) = | x + 2 | tan − 1 ( x + 2 ) , x ≠ − 2 2 , x = – 2 then f ( x ) is

f ( x ) = sin − 1 2 x 1 + x 2 is differentiable on

If f ( x ) = 1 , x < 0 1 + sin x , 0 ≤ x < π 2 , Then f ′ ( 0 ) i s

If f ( x ) = a | sin x | + b e | x | + c | x | 3 andif f ( x ) is differentiableat x = 0 ,then

The function f ( x ) = 1 − 1 − x 2 is

If f ( x ) = ( x + 1 ) cot x is continuous at x = 0 , then f ( 0 ) is

The function f ( x ) = e 1 / x − 1 e 1 / x + 1 , x ≠ 0 is 0 , x = 0

The function f ( x ) = | x | + | x − 1 | is

Let f ( x ) = 2 x 3 − 5 . Then, number of points of discontinuity of f ( x ) in ( 1 , 2 )

The function f ( x ) = | x − 3 | , x ≥ 1 x 2 4 − 3 x 2 + 13 4 , x < 1

f ( x ) = | ⌈ x ] x | in − 1 ≤ x ≤ 2 is

Let [ . ] denote the greatest integer function and f ( x ) = tan 2 x . Then,

The function f ( x ) = x 2 − 1 x 2 − 3 x + 2 + cos ( | x | ) is not differentiable at:

Let f ( x ) = a x 2 + 1 f o r x > 1 x + a f o r x ≤ 1 then f ( x ) is derivable at x = 1 , if

If f ( x ) = ∫ x + sin x x + cos x d x , then lim x ∞ f ( x ) =

The left hand derivative of f ( x ) = [ x ] sin ( π x ) a t x = k , k an integer, is

If f is differentiable function, the value of lim h 0 f x + h 2 − f x 2 2 h is equal to

The function defined by f x = x sin 1 x for x ≠ 0 0 for x = 0 at x = 0 is

f ( x ) = x 3 − log sin x x − 2 to be continuous at x = 0 then f ( 0 ) =

If f ( x ) = x α cos 1 x , if x ≠ 0 0 , if x = 0 is continuous at x = 0 then

f ( x ) = min x , x 2 ∀ x ∈ R then f ( x ) is

The function f ( x ) = cos − 1 ( cos x ) is

If f ( x ) = ( x − a ) g ( x ) and g ( x ) is continuous at x = a then f 1 ( a ) =

The function f ( x ) = [ x ] 2 − x 2 (where [ y ] is the tangent integer ≤ y ) is discontinuous at

If f ( x ) = 1 x 2 − 17 x + 66 then f 2 x − 2 is discontinuous at x is equal to

Let the function f ( x ) = sin 3 x 2 x ∀ x ≠ 0 0 ∀ x = 0

If a function f ( x ) is defined as f ( x ) = x x 2 , x ≠ 0 0 , x = 0 then

If f ( x ) = x e x then at x = 0

If f : R R is even function which is twice differentiable on R and f 11 ( π ) = 1 then f 11 − π is

If f ( x ) = − 3 x + 2 , x < 1 1 2 x 2 + 7 , x ≥ 1 then which of the following is not true

If x = sint and y = sinpt then the value of 1 − x 2 d y d x 2 − x d y d x + p 2 y =

If sec x − y x + y = a then d y d x =

y = Tan − 1 1 − x 1 + x then d y d cos − 1 x =