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Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Commerce MCQ


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10 Questions MCQ Test Mathematics (Maths) Class 11 - Test: Limits and Derivatives (Derivatives)- Case Based Type Questions

Test: Limits and Derivatives (Derivatives)- Case Based Type Questions for Commerce 2024 is part of Mathematics (Maths) Class 11 preparation. The Test: Limits and Derivatives (Derivatives)- Case Based Type Questions questions and answers have been prepared according to the Commerce exam syllabus.The Test: Limits and Derivatives (Derivatives)- Case Based Type Questions MCQs are made for Commerce 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Limits and Derivatives (Derivatives)- Case Based Type Questions below.
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Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 1

The derivative of y with respect to x is the change in y with respect to a change in x.

The derivative of f(x) at x0 is given by

Based on the above data, answer the following question.

Q. Derivative off tan x w.r.t. x is ............

Detailed Solution for Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 1
Let f(x) = tan x = sin x / cos x

=

= sec2 x

Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 2

The derivative of y with respect to x is the change in y with respect to a change in x.

The derivative of f(x) at x0 is given by

Based on the above data, answer the following question.

Q. y = x / tanx , dy / dx = ........

Detailed Solution for Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 2

Let

dy/dx =

=

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Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 3

The derivative of y with respect to x is the change in y with respect to a change in x.

The derivative of f(x) at x0 is given by

Based on the above data, answer the following question.

Q. Derivative of sin x with respect to x is ..........

Detailed Solution for Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 3
Derivative of sin x with respect to x is cos x.
Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 4

The derivative of y with respect to x is the change in y with respect to a change in x.

The derivative of f(x) at x0 is given by

Based on the above data, answer the following question.

Q. Derivative of cos x with respect to x is ...............

Detailed Solution for Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 4

Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 5

The derivative of y with respect to x is the change in y with respect to a change in x.

The derivative of f(x) at x0 is given by

Based on the above data, answer the following question.

Q. If f(x) = x100 – x80, f '(1) is ...........

Detailed Solution for Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 5

f(x) = x100 – x50 f'(x)

= 100x99 – 50x49 f'(1)

= 100 – 50 = 50

Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 6

Indeterminate forms of limits

On direct evaluation, if a limit takes the form 0 /0,∞ /∞,0 ×∞ ..., we use standard results for evaluating the limits. The below figure shows a few indeterminate forms.

Based on the above data, answer the following question.

Q.

Detailed Solution for Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 6

=

=

= 3

Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 7

Indeterminate forms of limits

On direct evaluation, if a limit takes the form 0 /0,∞ /∞,0 ×∞ ..., we use standard results for evaluating the limits. The below figure shows a few indeterminate forms.

Based on the above data, answer the following question.

Q.

Detailed Solution for Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 7

=

=

= –2 × 1 × 1 × 6 = –12

Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 8

Indeterminate forms of limits

On direct evaluation, if a limit takes the form 0 /0,∞ /∞,0 ×∞ ..., we use standard results for evaluating the limits. The below figure shows a few indeterminate forms.

Based on the above data, answer the following question.

Q.

Detailed Solution for Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 8

=

Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 9

Indeterminate forms of limits

On direct evaluation, if a limit takes the form 0 /0,∞ /∞,0 ×∞ ..., we use standard results for evaluating the limits. The below figure shows a few indeterminate forms.

Based on the above data, answer the following question.

Q.

Detailed Solution for Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 9

=

= log 8 – log 2

= log 8/2

= log 4

Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 10

Indeterminate forms of limits

On direct evaluation, if a limit takes the form 0 /0,∞ /∞,0 ×∞ ..., we use standard results for evaluating the limits. The below figure shows a few indeterminate forms.

Based on the above data, answer the following question.

Q.

Detailed Solution for Test: Limits and Derivatives (Derivatives)- Case Based Type Questions - Question 10

= 6 × 25 = 192

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