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Limits of
trigonometric functions |
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Evaluating
trigonometric
limits, examples |
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Limits of functions
based on the definition of the natural number e |
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Evaluating
limits of functions
based on the definition of the natural number e |
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| Evaluating
trigonometric
limits, examples |
| We
use the fundamental limit |
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and
known trigonometric identities when solving
trigonometric |
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limits.
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| Example: Evaluate
the limit |
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| Solution:
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| Example: Evaluate
the limit |
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| Solution:
Since
cos (a
+ b)
= cosa cosb
-
sina sinb
then cos2a
= cos2a
-
sin2a
= 1 -
2sin2a |
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is |
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| Example: Evaluate
the limit |
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| Solution:
We
use the sum to product identity and the fundamental
trigonometric limit, thus |
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| Example: Evaluate
the limit |
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| Solution:
If
we substitute arcsin
(x
+ 2) = t
then, |
| x
+ 2 = sin t or
x =
sin t -
2 so that, t
®
0 as
x ®
-2,
therefore |
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Evaluating
limits of functions
based on the definition of the natural number e
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| Use |
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to
evaluate limits of the form |
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| Example: Evaluate
the limit |
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| Solution:
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| Example: Evaluate
the limit |
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| Solution:
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