To understand Limit in Calculus we need to learn various Laws of Limit. Limits have several different types of laws the very first law is constant law.
Constant law: Suppose we have f(x) =b (where f is constant for all x) then the limits as 'x' approaches 'c' must be equal to b.
: If b and c are constant: lim x→c b =b
Identity rule: According to this law, if f(x) =x, then the limit of f as x approaches c is equal to c.
If c is a constant: lim x→c x =c.
Special law of Operational Identities: Ø Suppose we have lim x→c f(x) =L and lim x→c g(x) =M and k is constant then the limit is,
Constant multiple law: lim x→c kf(x) = k. lim x→c f(x) =kL
Addition law: lim x→c [f(x) +g(x)] = lim x→c f(x) + lim x→c g(x) =L+M
Difference Law: lim x→c [f(x) -g(x)] = lim x→c f(x) - lim x→c g(x) =L-M
Product Law: lim x→c [f(x)g(x)] = lim x→c f(x) lim x→c g(x) =LM
Quotient law: lim x→c [f(x) /g(x)] = lim x→c f(x) / lim x→c g(x) =L/M (where M is not equal to zero.)
This is a brief definition of the laws of limits.