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# Test: Introduction And Algebra Of Limits

## 10 Questions MCQ Test Mathematics For JEE | Test: Introduction And Algebra Of Limits

Description
This mock test of Test: Introduction And Algebra Of Limits for JEE helps you for every JEE entrance exam. This contains 10 Multiple Choice Questions for JEE Test: Introduction And Algebra Of Limits (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: Introduction And Algebra Of Limits quiz give you a good mix of easy questions and tough questions. JEE students definitely take this Test: Introduction And Algebra Of Limits exercise for a better result in the exam. You can find other Test: Introduction And Algebra Of Limits extra questions, long questions & short questions for JEE on EduRev as well by searching above.
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

Solution:

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.

QUESTION: 2

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

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

QUESTION: 3

### Solution:

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

QUESTION: 4

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

Solution:

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

QUESTION: 5

Let f be any function, such that exists, then Solution:

lim(x → a) f(x) = l
λf(x) = λl

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

Solution:

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)

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.​

Solution:
QUESTION: 8

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

Solution:

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

QUESTION: 9

The value of Solution: 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.​ Solution: