Continuity and Differentiability Test

Result

Continuity and Differentiability Test - 5

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Weekly Quiz Competition

Question 1
1 / -0.25

The dervative of y

A

B

C

D
Question 2
1 / -0.25

Differentiate with respect to x.

A

B

C

D

Solution

y = e^(-x)² .................(1)
Put u = (-x)²
du/dx = -2x dx
Differentiating eq(1) y = e^u
dy/du = e^u
⇒dy/dx = (dy/du) * (du/dx)
= (e^u ) * (-2x)
⇒- 2xe^(-x2)
Question 3
1 / -0.25

The derivatve of f(x) =

A

B

C

D
3x²

Solution

f(x) = e^log(logx3)
As log and e are inverse operations, therefore
f(x)= logx³
So derivative will be {Derivative of log x is 1/x and then applying chain rule}

f ’(x)=1/x³ . 3x² = 3/x
Question 4
1 / -0.25

The sum of Which series is denoted by e.

A

B

C

D
Question 5
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Derivatve of f(x) is given by

A

B

C

D

Solution

y
The derivative of y = e^f(x) is dy/dx = f '(x)e^f(x)
In this case, f(x) = x² , and the derivative of x² = 2x
Therefore, f '(x)= 2x,
dy/dx = 2x
Question 6
1 / -0.25

The differential equation of y =

A

B

C
log(1 - y)

D
none
Question 7
1 / -0.25

If f(x) = e^2x-5 , then f '(x) is

A
5 e^{2x –5}

B
2 e^{2x –5}

C
log (2x –5)

D
2 log (2x –5)
Question 8
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Whta is the derivatve of y = log₅ (x)

A

B

C

D

Solution

y = log5 x = ln x/ln 5 →change of base
= ln x/ln 5
dy/dx = 1/ln5 ⋅1/x →1/ln5 is a constant, so we don 't change it
= 1/(x ln 5)
Question 9
1 / -0.25

For what values of x is e^logx = x

A
Set of all positive real numbers

B
Set of all real numbers

C
Set of all negative real numbers

D
Set of all numbers

Solution

The correct option is A
Set of all positive real numbers
Question 10
1 / -0.25

If f(x) = e^x , then the value of f '(-3) is

A
log (3)

B
e²

C
log (-3)

D
e^-3

Solution

As, f (x) = e^x
Similarly, f (-3) = e^-3