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
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.
If f(x) = 2, then
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
For the limit of a function to exist we must have
Recall for a limit to exist, the left and right limits must exist (be finite) and be equal.
Let f be any function, such that exists, then
lim(x → a) f(x) = l
λf(x) = λl
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
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)
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.
As x → a, f(x) → l, then l is called the……..of the function f(X) which is symbolically written as…….
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
The value of
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.
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