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free/or 0.5$ |
| m97346 | Use a CAS to evaluate the definite integrals in Problems. If the CAS does not give an exact answer in term of elementary function, give a numerical approximation.
(a)
(b)
(c)
(d) |
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| m97347 | Use a CAS to evaluate the limits in Problems 34-37?
1.
2.
3.
4. |
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| m97348 | Use a CAS to find the first four nonzero terms in the Maclaurin series for each of the following. Check Problems 1-4 to see that you get the same answers using the methods of Section 9.7?
1. Sin (Exp x - 1)
2. Exp (Sin x)
3. (Sin x) (Exp x)
4. (Sin x) / (Exp x) |
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| m97349 | Use a CAS to solve each of the following equations:
1. Y" - 4y - 6y = 0; y(0) = 1, y (0) = 2
2. Y" + 5y + 6.25y = 0; y(0) = 2, y (0) = - 1,5
3. 2y" + y + 2y = 0; y(0) = 0, y (0) = 1.25 |
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| m97351 | Use a computer or a graphing calculator to find the limits in Problems 1-3. Begin by plotting the function in an appropriate window.
1.
2.
3. |
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| m97354 | Use a graphing calculator to plot the graph of the integrand in Problems. Then estimate the integral as suggested in the margin note accompanying Theorem B.
(a)
(b)
(c)
(d) |
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| m97356 | Use a line integral to find the area of the part cut out of the vertical square cylinder |x| + |y| = a by the sphere x2 + y2 + z3 = z2. Check your answer by finding a trivial way to do this problem. |
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| m97357 | Use a line intergral to find the area of that part of the cylinder x2 + y2 = ay inside the sphere x2 = y2 + z2 = a2. |
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| m97358 | Use a Maclaurin polynomial to obtain the approximation A ( r2t3 / 12 for the area of the shaded region in Figure 5. First express A exactly, then approximate. |
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| m97360 | Use
(a) The Trapezoidal Rule,
(b) The Midpoint Rule, and
(c) Simpson’s Rule with n = 10 to approximate the given integral, round your answers to six decimal places.
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| m97361 | Use a transformation to evaluate the integral
Where R is the rectangle with vertices (0, 0), ((/2, -(/2), ((, 0), and ((/2, (/2). |
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| m97363 | Use a y-integration to find the length of the segment of the line 2y - 2x + 3 = 0 between y = 1 and y = 3. Check by using the distance formula. |
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| m97364 | Use an x-integration to find the length of the segment of the line y = 2x + 3 between x = 1 and x = 3. Check by using the distance formula. |
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| m97365 | Use diagrams, as in Figure 1, to show that |
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| m97366 | Use diagrams, as in Figure 1, to show that
Show that the sequence
In increasing and bounded above by 1? |
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| m97367 | Use Euler s Method with h = 0.2 to approximate the solution to the differential equation y = xy with initial condition y(1) = 2 over the interval [1, 2] |
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| m97368 | Use Example 3 to develop a formula for the area of the triangle with vertices P(a, 0, 0), Q(0, b, 0), Q(0, b, 0), and R(0, 0, c) shown in the left half of Figure 6. |
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| m97369 | Use Figure 6.
(a) Find Q as a function of time. Assume that the capacitor is initially uncharged.
(b) Find I as a function of time. |
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| m97370 | Use Fubini s Theorem to derive an expression for the volume of a set in R3 obtained by revolving a Jordan measurable set in the yz -plane about the -axis. |
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| m97371 | Use Fubini s Theorem to give an easy proof that D1, 2f = D2, 1f if these are continuous. |
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