Evaluation of Limits MCQ Quiz - Objective Question with Answer for Evaluation of Limits - Download Free PDF
Last updated on Apr 22, 2025
Latest Evaluation of Limits MCQ Objective Questions
Evaluation of Limits Question 1:
If y = In(emx + e-mx), then what is the value of
Answer (Detailed Solution Below)
Evaluation of Limits Question 1 Detailed Solution
Concept:
If y = ln f(x) then
Calculation:
Given function is y = ln(emx + me-mx)
Differentiating, we get
At x = 0, we have
⇒
∴ For y = ln(emx + me-mx),
Evaluation of Limits Question 2:
If
Answer (Detailed Solution Below)
Evaluation of Limits Question 2 Detailed Solution
Concept:
Chain Rule:
- If y = f(g(x)), then dy/dx = f '(g(x) × g'(x)
- If y = p(x)/q(x), then dy/dx =
Formula used:
- (log x)' = 1/x
- (xn)' = n xn-1
Calculation:
If
then,
⇒
⇒
⇒
⇒
⇒
⇒
∴ The correct answer is option (4).
Evaluation of Limits Question 3:
Answer (Detailed Solution Below)
Evaluation of Limits Question 3 Detailed Solution
Explanation:
Given:
L =
Taking log on both side we get
log L =
Taking RHS
Using L'hospital's Rule we get
=
Again using L'hospital's Rule we get
=
So we can see that L does not exist.
Evaluation of Limits Question 4:
is equal to
Answer (Detailed Solution Below)
Evaluation of Limits Question 4 Detailed Solution
Calculation
Using L’hopital rule
Hence option 3 is correct
Evaluation of Limits Question 5:
What is the value of
Answer (Detailed Solution Below)
Evaluation of Limits Question 5 Detailed Solution
Formula used
a3 - b3 = (a - b)(a2 + ab + b2)
Calculation
Givn
x3 - 1728 = (x - 12)(x2 + 12x + 144)
⇒
⇒
Now, substituting x = 12
⇒ 122 + 12 (12) + 144 = 144 + 144 + 144 = 432
∴ The value of the limit is: 432
Top Evaluation of Limits MCQ Objective Questions
What is the value of
Answer (Detailed Solution Below)
Evaluation of Limits Question 6 Detailed Solution
Download Solution PDFConcept:
- 1 - cos 2θ = 2 sin2 θ
Calculation:
=
=
=
= 4 × 1 = 4
Answer (Detailed Solution Below)
Evaluation of Limits Question 7 Detailed Solution
Download Solution PDFConcept:
Calculation:
As we know
Therefore,
Hence
Answer (Detailed Solution Below)
Evaluation of Limits Question 8 Detailed Solution
Download Solution PDFCalculation:
We have to find the value of
This limit is of the form
=
Factor x becomes ∞ at x tends to ∞, So we need to cancel this factor from numerator and denominator.
=
=
Answer (Detailed Solution Below)
Evaluation of Limits Question 9 Detailed Solution
Download Solution PDFCalculation:
We have to find the value of
This limit is of the form
=
Factor x2 becomes ∞ at x tends to ∞, So we need to cancel this factor from numerator and denominator.
=
=
The value of
Answer (Detailed Solution Below)
Evaluation of Limits Question 10 Detailed Solution
Download Solution PDFConcept:
. . . .
Indeterminate Forms: Any expression whose value cannot be defined, like
- For the indeterminate form
, first try to rationalize by multiplying with the conjugate, or simplify by cancelling some terms in the numerator and denominator. Else, use the L'Hospital's rule. - L'Hospital's Rule: For the differentiable functions f(x) and g(x), the
, if f(x) and g(x) are both 0 or ±∞ (i.e. an Indeterminate Form) is equal to the if it exists.
Calculation:
We know that
∴
What is
Answer (Detailed Solution Below)
Evaluation of Limits Question 11 Detailed Solution
Download Solution PDFConcept:
log mn = n log m
Calculation:
Answer (Detailed Solution Below)
Evaluation of Limits Question 12 Detailed Solution
Download Solution PDFFormula used:
Calculation:
Since, 1 - cos 2θ = sin2θ
⇒
⇒
∴
Find the value of
Answer (Detailed Solution Below)
Evaluation of Limits Question 13 Detailed Solution
Download Solution PDFConcept:
Calculation:
=
=
Let
If x → ∞ then t → 0
=
= 1 × π
= π
What is
Answer (Detailed Solution Below)
Evaluation of Limits Question 14 Detailed Solution
Download Solution PDFConcept:
Calculation:
We have to find the value of
As we know,
= 1 ×
=
=
= -1 × 1
= -1
Answer (Detailed Solution Below)
Evaluation of Limits Question 15 Detailed Solution
Download Solution PDFThis can be written as:
Taking 3n common, we can write:
Here
So,