Test: Introduction And Algebra Of Limits - JEE MCQ

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.

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

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

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

lim(x → a) f(x) = l
λf(x) = λl 

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)

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

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

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

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