Continuity and Differentiability Test

Result

Continuity and Differentiability Test - 6

Score
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out of -
Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0.25

A
1/2

B
0

C
1

D
none of these

Solution
Question 2
1 / -0.25

A
0

B
1

C
does not exist

D
none of these

Solution
Question 3
1 / -0.25

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

A
all x ∈I

B
all x ∈(R −I)

C
all x ∈R

D
all x ∈Rx- {0]

Solution

f(x) = x -[x] is derivable at all x ∈ R –I , and f ‘(x) = 1 for all x ∈ R –I .
Question 4
1 / -0.25

f (x) = max {x, x³ },then the number of points where f (x) is not differentiable, are

A
1

B
2

C
3

D
4

Solution

f(x)=m{x,x³ }
= x;x <−1 and
= x³ ;−1 ≤x ≤0
⇒f(x)=x;0 ≤x ≤1 and
= x³ ;x ≥1
∴f(x)=1;x <−1
∴f ′(x)=3x² ;−1 ≤x ≤0 and =1
0 Hence answer is 3
Question 5
1 / -0.25

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

A
f (x) = g (x)

B
f ‘(x) = g ‘(x)

C
f ''(x) = g ''(x)

D
none of these

Solution
Question 6
1 / -0.25

A
1/2

B
1

C
0

D
none of these

Solution
Question 7
1 / -0.25

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

A
differentiable everywhere.

B
continuous everywhere

C
continuous nowhere

D
differentiable nowhere

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
1 / -0.25

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

A
25

B
1

C
30

D
none of these

Solution
Question 9
1 / -0.25

A
e³

B
e^1/3

C
3 e

D
none of these

Solution
Question 10
1 / -0.25

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

A

B

C

D
none of these

Solution

d/dx(log|x|)
= 1/|x|