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ALGEBRA
- solved problems |
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The
limit of a function
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The limit of a rational function at infinity
containing roots (irrational expressions)
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Evaluate
the limit |
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Solution: |
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Evaluate
the limit |
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Solution: |
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The limit of a rational function at a point containing
irrational expressions, use of substitution |
Use of the method of substitution to avoid the indeterminate form of an expression. |
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Evaluate
the limit |
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Solution:
Let substitute,
x
+ 1 = y6,
then as x
®
0 then
y
®
1,
therefore |
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Evaluate
the limit |
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Solution:
Let substitute,
x
= y12,
then as x
®
1 then
y
®
1,
therefore |
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Evaluate
the limit |
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Solution:
Let rationalize
the numerator, |
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Evaluate
the limit |
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Solution:
Let rationalize
both the numerator
and denominator, |
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Evaluating
trigonometric
limits |
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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Evaluate
the limit |
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Evaluate
the limit |
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Solution:
Since
cos(a
+ b)
= cosacosb
-
sinasinb
then cos2a
= cos2a
-
sin2a
= 1 -
2sin2a |
that
is |
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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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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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Solved
problems contents - A |
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