For the initial value problem, compute the first two approximations u1 and u2 given by Euler's method using the given time step.y'(t) = -y, y(0) = -5; ?t = 0.5
A. u1 = -5; u2 = -2.5
B. u1 = -2.5; u2 = -1.25
C. u1 = -2.5; u2 = -2.5
D. u1 = 0; u2 = -2.25
Answer: B
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Show that the set has cardinal number ?0 by establishing a one-to-one correspondence between the natural numbers and the given set. Be sure to indicate the general correspondence.{0, 3, 6, 9, 12, ...}
A.
| 1, | 2, | 3, | 4, | ..., | n, | ... |
| ? | ? | ? | ? | ? |
| 0, | 3, | 6, | 9, | ..., | 3n - 3, ... |
B.
| 1, | 2, | 3, | 4, | ..., | n, | ... |
| ? | ? | ? | ? | ? |
| 0, | 3, | 6, | 9, | ..., | 3n, | ... |
C.
| 1, | 2, | 3, | 4, | ..., | n, | ... |
| ? | ? | ? | ? | ? |
| 0, | 3, | 6, | 9, | ..., | 3n - 1, ... |
D.
| 1, | 2, | 3, | 4, | ..., | n, | ... |
| ? | ? | ? | ? | ? |
| 0, | 3, | 6, | 9, | ..., | 3n + 3, ... |
Solve the equation and express the solution in exact form using either ln or log as indicated.
x = 16
Express the answer using ln.
A. 
B. 
C. 
D. 
Use factoring to find f(x) and g(x) so that h(x) = f(x)g(x).x2 + 3x - 108
A. f(x) = x - 12, g(x) = x + 1 B. f(x) = x - 12, g(x) = x - 9 C. f(x) = x + 12, g(x) = x - 9 D. f(x) = x - 12, g(x) = x + 9
An arithmetic sequence is given. Find the common difference and write out the first four terms.{7n + 6}
A. d = 6; 7, 13, 20, 27 B. d = 7; 7, 13, 20, 27 C. d = 6; 13, 20, 27, 34 D. d = 7; 13, 20, 27, 34