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This mock test of Test: Continuity And Differentiability (CBSE Level) - 1 for JEE helps you for every JEE entrance exam.
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QUESTION: 1

Solution:

QUESTION: 2

Solution:

QUESTION: 3

Let f(x) = x – [x], then f ‘ (x) = 1 for

Solution:

f(x) = x -[x] is derivable at all x ∈ R – I , and f ‘(x) = 1 for all x ∈ R – I .

QUESTION: 4

f (x) = max {x, x^{3}},then the number of points where f (x) is not differentiable, are

Solution:

f(x)=m{x,x^{3}}

= x;x<−1 and

= x^{3};−1≤x≤0

⇒ f(x)=x;0≤x≤1 and

= x^{3};x≥1

∴ f(x)=1;x<−1

∴ f′(x)=3x^{2};− 1≤x≤0 and =1

0<x<1

Hence answer is 3

QUESTION: 5

If f(x) = tan^{-1}x and g(x) = , then

Solution:

QUESTION: 6

Solution:

QUESTION: 7

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

Solution:

f(x) = 1+|sinx| is not derivable at those x for which sinx = 0, however, 1+|sinx| is continuous everywhere (being the sum of two continuous functions)

QUESTION: 8

Let f (x + y) = f(x) + f(y) ∀ x, y ∈ R. Suppose that f (6) = 5 and f ‘ (0) = 1, then f ‘ (6) is equal to

Solution:

QUESTION: 9

Solution:

QUESTION: 10

Derivative of log | x | w.r.t. | x | is

Solution:

d/dx(log|x|)

= 1/|x|

QUESTION: 11

Solution:

QUESTION: 12

The function, f (x) = (x – a) sin for x ≠ a and f (a) = 0 is

Solution:

QUESTION: 13

If x sin (a + y) = sin y, then is equal to

Solution:

x sin(a+y) = sin y

⇒

QUESTION: 14

Solution:

QUESTION: 15

Solution:

QUESTION: 16

If [x] stands for the integral part of x, then

Solution:

If c is an integer , then Does not exist.

QUESTION: 17

Let f (x) = [x], then f (x) is

Solution:

f(x) = [x] is derivable at all x except at integral points i.e. on R – I .

QUESTION: 18

Solution:

QUESTION: 19

Solution:

QUESTION: 20

Solution:

QUESTION: 21

Solution:

QUESTION: 22

The function f (x) = [x] is

Solution:

The function f (x) = [x] isdiscontinuous only for all integral values of x.

QUESTION: 23

Let f be a function satisfying f(x + y) = f(x) + f(y) for all x, y ∈ R, then f ‘ (x) =

Solution:

QUESTION: 24

Solution:

QUESTION: 25

If x = at^{2}, y = 2at, then is equal to

Solution:

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