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| ALGEBRA
- solved problems |
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The
limit of a function
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| Limits of
functions
properties |
| Assume that |
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exist
and that c
is any constant. Then, |
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11.
Squeeze rule |
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If f
(x)
< g (x) < h (x)
for all x
in an open interval that contains a,
except possibly at x
= a, |
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and |
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then |
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12.
Composition rule |
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If f
(x)
is continuous at x
= b
and |
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then, |
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| Limits of
functions
properties use |
| Limits
that are commonly used are written below for easy reference, |
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| By
comparing the area of the sector of the arc x
with areas
of the two right triangles, the smaller triangle
with
legs sin x
and cos x,
and the bigger triangle with legs
tan x
and 1, shown on the right figure, we get |
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| Since
the left and the right side of the last
inequality tend
to the same limit 1, as x
tends to 0 then, applying
the squeeze rule obtained is |
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fundamental or basic trigonometric limit.
Note
that the arc length x
is measured in radians. |
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since both
factors on the right tend to 1, as x
tends to 0, then |
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| Solved
problems contents - A |
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