| № |
Condition |
free/or 0.5$ |
| m53553 | Determine whether the series is conditionally convergent, absolutely convergent, or divergent.
a.
b. |
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| m53554 | Determine whether the series is convergent or divergent.
(a)
(b) 1 + 1/8 + 1/27 + 1/64 + 1/125 + ...
(c) 1 + 1/3 + 1/5 + 1/7 + 1/9 + ... |
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| m53555 | Determine whether the series is convergent or divergent.
a.
b.
c. |
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| m53556 | Determine whether the series is convergent or divergent by expressing Sn as a telescoping sum (as in Example 7). If it is convergent, find its sum.
a.
b.
c. |
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| m53557 | Determine whether the series is convergent or divergent. If it is convergent, find its sum.
a. 1/3 + 1/6 + 1/9 + 1/12 + 1/15 + ....
b.
c. |
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| m53572 | Differentiate.
(a) f(x) = 3x2 - 2 cos x
(b) f(x) = sin x + 1/2 cot x
(c) y = sec θ tan θ |
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| m53573 | Differentiate.
(a) f(x) = (x3 + 2x)ex
(b) y = x/ ex
(c) g(x) = 1 + 2x / 3 - 4x |
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| m53574 | Differentiate each trigonometric identity to obtain a new (or familiar) identity.
(a) tan x = sin x / cos x
(b) sec x = 1/cos x
(c) sin x + cos x = 1 + cot x/csc x |
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| m53575 | Differentiate f and find the domain of f.
(a) f(x) = x/ 1 - ln(x - 1)
(b) f(x) = ln(x2 - 2x) |
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| m53576 | Differentiate the function.
(a) f(x) = 240
(b) f(t) = 2 - 2/3t
(c) f(x) = x3 - 4x + 6
(d) g(x) = x2 (1 - 2x) |
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| m53577 | Differentiate the function.
(a) f(x) = sin (ln x)
(b) f(x) = ln 1/x
(c) f(x) = log10(x3 + 1) |
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| m53579 | Discuss four ways of representing a function. Illustrate your discussion with examples. |
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| m53594 | Do the graphs intersect in the given viewing rectangle? If they do, how many points of intersection are there?
y = 3x2 - 6x + 1, y = 0.23x - 2.25; [-1, 3] by [-2.5, 1.5] |
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| m53601 | Does there exist a function f such that f(0) = - 1, f(2) = 4, and f (x) ≤ 2for all x? |
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| m53607 | Draw a diagram to show that there are two tangent lines to the parabola y = x2 that pass through the point (0, - 4). Find the coordinates of the points where these tangent lines intersect the parabola. |
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| m53608 | Draw a picture to show that
What can you conclude about the series? |
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| m53609 | Draw, by hand, a rough sketch of the graph of each function.
(a) y = sin x
(b) y = tan x
(c) y = ex
(d) y = ln x
(e) y = 1/x
(f) y = | x |
(g) y = sx
(h) y = tan-1 x |
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| m53611 | Draw the graph of the equation x + |x| = y + |y|. |
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| m53622 | Each integral represents the volume of a solid. Describe the solid.
(a)
(b) |
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| m53623 | Each integral represents the volume of a solid. Describe the solid.
(a)
(b) |
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