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AlgebraicLimitsand Continuity
1.2
OBJECTIVE
• Develop and use the Limit Principles to calculate limits.
• Determine whether a function is continuous at a point.
2012 Pearson Education, Inc.
All rights reserved Slide 1.2-2
1.2AlgebraicLimitsandContinuity
LIMIT PROPERTIES:
If
lim f(x) = L x®a
and
limg(x) = M x®a
then
we have the following:
L.1
limc = c x®a
The limit of a constant is the constant.
2012 Pearson Education, Inc. All rights reserved Slide 1.2-3
1.2AlgebraicLimitsandContinuity
LIMIT PROPERTIES (continued):
L.2 The limit of a power is the power of the limit, and the limit of a root is the root of the limit.
That is, for any positive integer n,
lim x a
f (x)]n
= lim f (x) n = L , x a
and
lim n f(x) = x®a
n lim f(x) = n L, x®a
assuming that L ≥ 0 when n is even.
2012 Pearson Education, Inc. All rights reserved Slide 1.2-4
1.2AlgebraicLimitsandContinuity
LIMIT PROPERTIES (continued):
L.3 The limit of a sum or difference is the sum or difference of the limits.
lim f(x)± g(x) = lim x®a x®a
f(x)± limg(x) = L ± M. x®a
L.4 The limit of a product is the product of the limits.
lim f(x)gg(x) = élim x®a x®a
f(x)ùglimg(x)ù = LgM. x®a
2012 Pearson Education, Inc. All rights reserved Slide 1.2-5
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