| № |
Condition |
free/or 0.5$ |
| m97636 | When no domain is given in the definition of a vector-valued function, it is to be understood that the domain is the set of all (real) scalars for which the rule for the function makes sense and gives real vectors (i.e., vectors with real components). Find the domain of each of the following vector-valued functions:
a.
b.
(|| ]Denotes the greatest integer function.)
c. |
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| m97644 | Where does the tangent line to y = (2x + 1)3 at (0, 1) cross the x-axis? |
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| m97645 | Where does the tangent line to y = (x2 + 1)-2 at (1, ¼) cross the x-axis? |
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| m97649 | Which of the following are odd function? Even function? Neither?
(a) t sin t
(b) sin2 t
(c) csc t
(d) |sin t|
(e) sin (csc t)
(f) x + sin x |
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| m97650 | Which of the following are odd function? Even functions Neither?
(a) cot t + sin t
(b) sin3 t
(c) sec t
(d) √sin4 t
(e) cos (sin t)
(f) x2 + sin x |
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| m97651 | Which of the following are true? Assume that x and y are real numbers.
(a) For every x, x > 0 ⇒ x2 > 0.
(b) For every x, x > 0 ⇔ x2 > 0.
(c) For every x, there exist a u such that y > x2.
(d) For every positive number y, there exists another positive number x such that 0 < x < y. |
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| m97652 | Which of the following are true? Unless it is stated other-wise, assume that x, y, and e are real numbers.
(a) For every x, x < x + 1.
(b) There exists a natural number N such that all prime numbers are less than N. (A prime number is a natural number whose only factors are 1 and itself.)
(c) For every x > 0, there exists a y such that y > 1
(d) For every positive x, there exists a natural number n such that - 1 < x.
(e) For every positive s, there exists a natural number n such that 1/2n < ε. |
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| m97654 | Which of the following function are odd? Even Neither even nor odd?
(a) f(x) = 3x / x2 + 1
(b) g(x) = |sin x| + cos x
(c) g(x) = x3 + sin x
(d) |
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| m97655 | Which of the following functions satisfies f(x + y) = f(x) + f(y) for all real numbers x and y?
(a) f(t) = 2t
(b) f(1) = t2
(c) f(t) = 2t + 1
(d) f(t) = - 3t |
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| m97656 | Which of the following represent the same graph? Check your result analytically using trigonometric identities.
(a) y = sin(x + π/2)
(b) y = cos(x + π/2)
(c) y = -sin(x + π)
(d) y = cos (x - π)
(e) y = -sin (π - x)
(f) y = cos (x - π/2)
(g) y = - cos (π - x)
(h) y = sin (x - π/2) |
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| m97657 | Which of the improper integrals converge?
1.
2.
3.
4.
5.
6. |
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| m97666 | Without doing any calculating, find each derivative.
(a) D4x(3x3 + 2x - 19)
(b) D12x(100 x11 - 79x10)
(c) D11x(x2 - 3)5 |
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| m97667 | Without doing any integration, find the median of the random variable that has PDF f(x) = 15/512x2(4 - x)2, 0 ≤ x ≤ 4. |
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| m97669 | Work Problem 34, assuming that the angle is 75o rather than 90o. |
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| m97679 | Write a sentence involving the word distance to express the following algebraic sentences:
(a) |x - 5| = 3
(b) |x + 1| ≤ 2
(c) |x - a| > b |
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| m97680 | Write a vector equation of the line through (2, -2, 1) and (-3, 2, 4). |
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| m97681 | Write an equation for the line through (3, - 3) that is
(a) Parallel to the line y = 2x + 5;
(b) Perpendicular to the line y = 2x + 5;
(c) Parallel to the line 2x + 3y = 6;
(d) Perpendicular to the line 2x + 3y = 6;
(e) Parallel to the line through (-1, 2) and (3, - 1); |
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| m97685 | Write the convene and the contrapositive to the following statements.
(a) If it rains today, then I will stay home from work.
(b) If the candidate meets all the qualifications, then she will be hired. |
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| m97686 | Write the converse and the contrapositive to the following statements.
(a) If I get an A on the final exam, I will pass the course.
(b) If I finish my research paper by Friday, then I will take off next week. |
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| m97687 | Write the converse and the contrapositive to the following statements.
(a) If the measure of angle ABC is 45°, then angle ABC is an acute angle.
(b) If a < b then a2 < b2. |
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