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Limits
The concept of limits is essential to calculus. The limit is
the basis for all calculus problems. A good understanding of
limits will help explain many theories in calculus.
Consider a function f defined for values of x, as x
gets close to a number a, not necessarily true for x = a.
If the value of f(x) approaches a number b as x
approaches a, then the limit of f(x) as x
approaches a is equal to b, denoted as :
limx®a
f(x) = b
ex.
Find the limit of f(x) = 3x + 2 as x approaches 3.
It is said that as x approaches 3, 3x approaches 9, and 3x + 2
approaches 11. Thus;
limx®3
3x + 2 = 11
Find the limit of f(x) = 1/ x - 3 as x approaches 3.
It is said that as x approaches 3, x - 3 approaches 0, and 1/
x - 3 approaches 1/ 0 which is undefined. Thus;
limx®3
1/x - 3 = undefined
In limits, the only thing that matters is how a function is
defined near the point a.
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