The right-hand limit of f (x), as x approaches a, equals L written: if we can make the value f (x)...
12
The right-hand limit of f (x), as x approaches a, equals L written : if we can make the value f (x) arbitrarily close to L by taking x to be sufficiently close to the right of a. a L One-Sided Limits lim () x a fx L () y fx
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Transcript of The right-hand limit of f (x), as x approaches a, equals L written: if we can make the value f (x)...
The right-hand limit of f (x), as x approaches a, equals L
written:
if we can make the value f (x) arbitrarily close to L by taking x to be sufficiently close to the right of a.
lim ( )x a
f x L
a
L( )y f x
One-Sided Limits
The left-hand limit of f (x), as x approaches a, equals M
written:
if we can make the value f (x) arbitrarily close to L by taking x to be sufficiently close to the left of a.
lim ( )x a
f x M
a
M
( )y f x
lim ( ) if and only if lim ( ) and lim ( ) .x a x a x a
f x L f x L f x L
Theorem
Find2
3 if 2lim ( ) where ( )
1 if 2x
x xf x f x
x
-2
6
Note: f (-2) = 1
Examples
1.
2.
3.
4.
2.6 Continuous and discontinuous functions A function f is continuous at a point x = a if the following are true:
) ( ) is definedi f a) lim ( ) exists
x aii f x
a
f(a)) lim ( ) ( )
x aiii f x f a
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