Test: Introduction And Algebra Of Limits - JEE MCQ

# Test: Introduction And Algebra Of Limits - JEE MCQ

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## 10 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Introduction And Algebra Of Limits

Test: Introduction And Algebra Of Limits for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Introduction And Algebra Of Limits questions and answers have been prepared according to the JEE exam syllabus.The Test: Introduction And Algebra Of Limits MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Introduction And Algebra Of Limits below.
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Test: Introduction And Algebra Of Limits - Question 1

### If the right and left hand limits coincide, we call that common value as the limit of f(x) at x = a and denote it by

Detailed Solution for Test: Introduction And Algebra Of Limits - Question 1

If the right-hand and left-hand limits coincide, we say the common value as the limit of f(x) at x = a and denote it by limx→a f(x) = l

• If limx→a- f(x) is the expected value of f at x = a given the values of ‘f’ near x to the left of a. This value is known as the left-hand limit of ‘f’ at a.

• If limx→a+ f(x) is the expected value of f at x = a given the values of ‘f’ near x to the right of a. This value is known as the right-hand limit of f(x) at a.

Test: Introduction And Algebra Of Limits - Question 2

### If f(x) = 2, then

Detailed Solution for Test: Introduction And Algebra Of Limits - Question 2

f(x) = 2
Hence it doesnt contain any variable
so, lim(x → 2) f(x) = 2

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Test: Introduction And Algebra Of Limits - Question 3
Detailed Solution for Test: Introduction And Algebra Of Limits - Question 3

lim(x → π ) (x - 22/7)
Taking limit, we get
⇒ π - 22/7

Test: Introduction And Algebra Of Limits - Question 4

For the limit of a function to exist we must have​

Detailed Solution for Test: Introduction And Algebra Of Limits - Question 4

Recall for a limit to exist, the left and right limits must exist (be finite) and be equal.

Test: Introduction And Algebra Of Limits - Question 5

Let f be any function, such that  exists, then

Detailed Solution for Test: Introduction And Algebra Of Limits - Question 5

lim(x → a) f(x) = l
λf(x) = λl

Test: Introduction And Algebra Of Limits - Question 6

Let f(x) and g(x) be two function, such that  and  exists, then the limit of the product of the function f(x) and g(x) is given by

Detailed Solution for Test: Introduction And Algebra Of Limits - Question 6

By algebric property of limits,
Limit of products = product of limits
lim(x → a) (f(x)*g(x)) = lim(x → a) f(x) * lim(x → a) g(x)

Test: Introduction And Algebra Of Limits - Question 7

is the expected value of f at x = a given the values of f near x to the left of a. This value is called the……….of f at a.​

Detailed Solution for Test: Introduction And Algebra Of Limits - Question 7

When the x approaches a negative, the limit is left hand limit.

Test: Introduction And Algebra Of Limits - Question 8

As x → a, f(x) → l, then l is called the……..of the function f(X) which is symbolically written as…….

Detailed Solution for Test: Introduction And Algebra Of Limits - Question 8

The number L is called the limit of function f(x) as x → a if and only if, for every ε>0 there exists δ>0
which is written as
lim (x → a) |f(x) − l|
lim (x → a) f(x) = l

Test: Introduction And Algebra Of Limits - Question 9

The value of

Detailed Solution for Test: Introduction And Algebra Of Limits - Question 9

After applying L'Hôpital's Rule and taking the limit as �x approaches 0, the limit of the derivatives is 3223​, which confirms our initial computation of the limit

Test: Introduction And Algebra Of Limits - Question 10

Consider the function f(x) = x + 10. Let us compute the value of the function f(x) for x very near to 5. Some of the points near and to the left of 5 and right to the 5 are given in the table.​

Detailed Solution for Test: Introduction And Algebra Of Limits - Question 10

4.9 approximately can be taken as 5,so we can take 5 as the function and the answer will be 15

## Mathematics (Maths) for JEE Main & Advanced

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## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests