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Test: Continuity and Differentiability- Case Based Type Questions


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10 Questions MCQ Test Mathematics (Maths) Class 12 | Test: Continuity and Differentiability- Case Based Type Questions

Test: Continuity and Differentiability- Case Based Type Questions for Commerce 2022 is part of Mathematics (Maths) Class 12 preparation. The Test: Continuity and Differentiability- Case Based Type Questions questions and answers have been prepared according to the Commerce exam syllabus.The Test: Continuity and Differentiability- Case Based Type Questions MCQs are made for Commerce 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Continuity and Differentiability- Case Based Type Questions below.
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Test: Continuity and Differentiability- Case Based Type Questions - Question 1

Direction: Read the following text and answer the following questions on the basis of the same:

A potter made a mud vessel, where the shape of the pot is based on f(x) = |x – 3| + |x – 2|, where f(x) represents the height of the pot.

If the potter is trying to make a pot using the function f(x) = [x], will he get a pot or not? Why?

Detailed Solution for Test: Continuity and Differentiability- Case Based Type Questions - Question 1 [x] is not continuous at integral values of x.
Test: Continuity and Differentiability- Case Based Type Questions - Question 2

Direction: Read the following text and answer the following questions on the basis of the same:

A potter made a mud vessel, where the shape of the pot is based on f(x) = |x – 3| + |x – 2|, where f(x) represents the height of the pot.

Will the slope vary with x value?

Detailed Solution for Test: Continuity and Differentiability- Case Based Type Questions - Question 2

Test: Continuity and Differentiability- Case Based Type Questions - Question 3

Direction: Read the following text and answer the following questions on the basis of the same:

A potter made a mud vessel, where the shape of the pot is based on f(x) = |x – 3| + |x – 2|, where f(x) represents the height of the pot.

When the value of x lies between (2, 3) then the function is

Detailed Solution for Test: Continuity and Differentiability- Case Based Type Questions - Question 3 In (2, 3), f(x) = 1
Test: Continuity and Differentiability- Case Based Type Questions - Question 4

Direction: Read the following text and answer the following questions on the basis of the same:

A potter made a mud vessel, where the shape of the pot is based on f(x) = |x – 3| + |x – 2|, where f(x) represents the height of the pot.

When x > 4 what will be the height in terms of x?

Detailed Solution for Test: Continuity and Differentiability- Case Based Type Questions - Question 4 The given function can be written as

When x > 4, f(x) = 2x – 5

Test: Continuity and Differentiability- Case Based Type Questions - Question 5

Direction: Read the following text and answer the following questions on the basis of the same:

A potter made a mud vessel, where the shape of the pot is based on f(x) = |x – 3| + |x – 2|, where f(x) represents the height of the pot.

What is dy/dx at x = 3

Detailed Solution for Test: Continuity and Differentiability- Case Based Type Questions - Question 5 f(x) is not differentiable at x = 2 and x = 3.
Test: Continuity and Differentiability- Case Based Type Questions - Question 6

Direction: Read the following text and answer the following questions on the basis of the same:

Ms. Remka of city school is teaching chain rule to her students with the help of a flow-chart

The chain rule says that if h and g are functions and f(x) = g(h(x)), then

Let f(x) = sin x and g(x) = x3

d/dx (sin2x) at x = π/2 is ____.

Detailed Solution for Test: Continuity and Differentiability- Case Based Type Questions - Question 6

= 2(-1)

= -2

Test: Continuity and Differentiability- Case Based Type Questions - Question 7

Direction: Read the following text and answer the following questions on the basis of the same:

Ms. Remka of city school is teaching chain rule to her students with the help of a flow-chart

The chain rule says that if h and g are functions and f(x) = g(h(x)), then

Let f(x) = sin x and g(x) = x3

gof(x) = _______.

Detailed Solution for Test: Continuity and Differentiability- Case Based Type Questions - Question 7 gof(x)

= g(f(x))

= g(sin x)

= sin3 x

Test: Continuity and Differentiability- Case Based Type Questions - Question 8

Direction: Read the following text and answer the following questions on the basis of the same:

Ms. Remka of city school is teaching chain rule to her students with the help of a flow-chart

The chain rule says that if h and g are functions and f(x) = g(h(x)), then

Let f(x) = sin x and g(x) = x3

d/dx sin x3 _______.

Detailed Solution for Test: Continuity and Differentiability- Case Based Type Questions - Question 8

= 3x2 cosx3

Test: Continuity and Differentiability- Case Based Type Questions - Question 9

Direction: Read the following text and answer the following questions on the basis of the same:

Ms. Remka of city school is teaching chain rule to her students with the help of a flow-chart

The chain rule says that if h and g are functions and f(x) = g(h(x)), then

Let f(x) = sin x and g(x) = x3

fog(x) = _______.

Detailed Solution for Test: Continuity and Differentiability- Case Based Type Questions - Question 9 fog(x)

= f(g(x))

= f(x3)

= sin (x3)

Test: Continuity and Differentiability- Case Based Type Questions - Question 10

Direction: Read the following text and answer the following questions on the basis of the same:

Ms. Remka of city school is teaching chain rule to her students with the help of a flow-chart

The chain rule says that if h and g are functions and f(x) = g(h(x)), then

Let f(x) = sin x and g(x) = x3

d/dx (sin3 x) = _______.

Detailed Solution for Test: Continuity and Differentiability- Case Based Type Questions - Question 10

= 3 sin2 x cos x

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