| № |
Condition |
free/or 0.5$ |
| m53510 | Describe the motion of a particle with position (x, y) as t varies in the given interval.
a. x = 3 + 2 cost, y = 1 + 2 sin t, π /2 ≤ t ≤ 3π /2.
b. x = 5 sin t, y= 2 cos t, -π ≤ t ≤ 5π |
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| m53511 | Describe the motion of a particle with position (x, y) as t varies in the given interval.
x = 5sint,
y = 2cos t,
-π ≤ t ≤ 5π |
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| m53515 | Determine
(a) By evaluating f(x) = 1/(x3 - 1) for values of that approach 1 from the left and from the right,
(b) By reasoning as in Example 9, and
(c) From a graph of f. |
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| m53517 | Determine a region whose area is equal to the given limit. Do not evaluate the limit. |
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| m53523 | Determine an appropriate viewing rectangle for the given function and use it to draw the graph.
F(x) = x2 - 36x + 32 |
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| m53524 | Determine how large the number has to be so that |
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| m53528 | Determine the infinite limit. |
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| m53538 | Determine the type of curve represented by the equation
x2 / k + y2 / k - 16 = 1
In each of the following cases:
(a) k > 16,
(b) 0 < k < 16,
(c) k < 0.
(d) Show that all the curves in parts (a) and (b) have the same foci, no matter what the value of is. |
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| m53541 | Determine whether each integral is convergent or divergent. Evaluate those that are convergent.
a.
b.
c. |
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| m53542 | Determine whether f is even, odd, or neither even nor odd.
(a) f(x) = 2x5 - 3x2 + 2
(b) f(x) = x3 - x7
(c) f(x) = e-x2
(d) f(x) = 1 + sin x |
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| m53543 | Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually.
F(x) = x /x2 + 1 |
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| m53544 | Determine whether f (0) exists. |
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| m53545 | Determine whether the differential equation is linear.
a. x - y = xy
b. y = 1 / x + 1 / y |
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| m53546 | Determine whether the differential equation is linear.
a. y + y = 1
b. y = x - y
c. xy + y = √x
d. sin x dy / dx (cos x) y = sin(x2)
e. (1 + t) du / dt + u = 1 + t, t > 0 |
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| m53547 | Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.
a. 3 - 4 + 16/3 - 64/9 + ...
b. 10 - 2 + 0.4 - 0.08 +...
c. 6(0.9) n-1 |
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| m53548 | Determine whether the sequence converges or diverges. If it converges, find the limit.
a. an = 1 - (0.2)n
b. an = 3 + 5n2 / n + n2
c. an = e1/n |
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| m53549 | Determine whether the sequence is convergent or divergent. If it is convergent, find its limit.
a.
b.
c. |
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| m53550 | Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?
a. an = 1 / 2n + 3
b. an = n(- 1)n
c. an = n / n2 + 1 |
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| m53551 | Determine whether the series converges or diverges.
(a)
(b)
(c) |
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| m53552 | Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
a.
b.
c. |
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