Limit Laws
Limit laws allow us to compute limits by breaking down complex
expressions into simple pieces, and then evaluating the limit one
piece at a time. These laws are really theorems that have been
proven, based on the technical definition of the limit.
Limit Laws
Suppose that limx→af(x) and
limx→ag(x) exist, and that c is a
constant. Then:
- The limit of a sum is the sum of the limits: limx→a(f(x)+g(x))=(limx→af(x))+(limx→ag(x)).
- The limit of a difference is the difference of the
limits: limx→a(f(x)−g(x))=(limx→af(x))−(limx→ag(x)).
- The limit of a multiple is a multiple of the limit:
limc→ac⋅f(x)=c⋅limx→af(x).
- The limit of a product is the product of the limits:
limx→a(f(x)⋅g(x))=(limx→af(x))⋅(limx→ag(x)).
- The limit of a quotient is the quotient of the limits
as long as you are not dividing by zero: limx→af(x)g(x)=limx→af(x)limx→ag(x), if limx→ag(x)≠0.
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Notice that the same rules apply to limits as x→a+ or x→a−.
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