| № |
Condition |
free/or 0.5$ |
| m52557 | (a) If f(x) = x √2 - x2, find f (x).
(b) Check to see that your answer to part (a) is reasonable by comparing the graphs of f and f |
buy |
| m52558 | (a) If f(x) = x √5 - x, find f (x).
(b) Find equations of the tangent lines to the curve y = x √5 - x at the points (1, 2) and (4, 4).
(c) Illustrate part (b) by graphing the curve and tangent lines on the same screen.
(d) Check to see that your answer to part (a) is reasonable by comparing the graphs of f and f . |
buy |
| m52559 | (a) If f(x) = (x2 - 1) /(x2 + 1), find f (x) and f" (x).
(b) Check to see that your answers to part (a) are reasonable by comparing the graphs of f, f and f" . |
buy |
| m52560 | (a) If f(x) = (x3 - x) ex, find f (x).
(b) Check to see that your answer to part (a) is reasonable by comparing the graphs of f and f . |
buy |
| m52561 | (a) If f(x) = x4 + 2x, find f (x).
(b) Check to see that your answer to part (a) is reasonable by comparing the graphs of and f . |
buy |
| m52562 | (a) If g(x) = 2x + 1 and h(x) = 4x2 + 4x + 7, find a function f such that f o g = h. (Think about what operations you would have to perform on the formula for to end up with the formula for h.)
(b) If f(x) = 3x + 5 and h(x) = 3x2 + 3x + 2, find a function g such that f o g = h. |
buy |
| m52563 | (a) If g(x) = (sin2x)/x2, use your calculator or computer to make a table of approximate values of
for t = 2, 5, 10, 100, 1000, and 10,000. Does it appear that
is convergent?
(b) Use the Comparison Theorem with f(x) = 1/x2 to show that
Is convergent.
(c) Illustrate part (b) by graphing f and g on the same screen for 1 ≤ x ≤ 10. Use your graph to explain intuitively why
is convergent. |
buy |
| m52564 | (a) If is a positive integer, prove that
d/dx (sinn x cos nx) = n sinn-1 x cos(n + 1)x
(b) Find a formula for the derivative of y = cosn x cos nx that is similar to the one in part (a). |
buy |
| m52565 | (a) If the function f(x) = x3 + ax2 + bx has the local minimum value -2/3 √3 at 1/√3, what are the values of a and b?
(b) Which of the tangent lines to the curve in part (a) has the smallest slope? |
buy |
| m52566 | (a) If the point (5, 3) is on the graph of an even function, what other point must also be on the graph?
(b) If the point (5, 3) is on the graph of an odd function, what other point must also be on the graph? |
buy |
| m52567 | (a) If the region shown in the figure is rotated about the x-axis to form a solid, use the Midpoint Rule with n = 4 to estimate the volume of the solid.
(b) Estimate the volume if the region is rotated about the y-axis. Again use the Midpoint Rule with n = 4. |
buy |
| m52568 | (a) If the symbol [ ] denotes the greatest integer function defined in Example 10, evaluate
(b) If n is an integer, evaluate
(c) For what values of does limx→a [x] exist? |
buy |
| m52569 | (a) If we shift a curve to the left, what happens to its reflection about the line y = x? In view of this geometric principle, find an expression for the inverse of g(x) = f(x + c), where f is a one-to-one function.
(b) Find an expression for the inverse of h(x) = f(cx), where c ≠ 0. |
buy |
| m52570 | (a) If we start from 0° latitude and proceed in a westerly direction, we can let T(x) denote the temperature at the point at any given time. Assuming that T is a continuous function of , show that at any fixed time there are at least two diametrically opposite points on the equator that have exactly the same temperature.
(b) Does the result in part (a) hold for points lying on any circle on the earth s surface?
(c) Does the result in part (a) hold for barometric pressure and for altitude above sea level? |
buy |
| m52571 | (a) Y,? is an unbiased estimator of µY. Is Y,? 2 an unbiased estimator of µ2Y?
(b) Y,? is a consistent estimator of µY. Is Y,? 2 a consistent estimator of µ2Y?
|
doc |
| m52572 | (a) In Example 11 the graphs suggest that the limaçon r = 1 + c sin θ has an inner loop when |c| > 1. Prove that this is true, and find the values of θ that correspond to the inner loop.
(b) From Figure 19 it appears that the limaçon loses its dimple when c = 1/2. Prove this. |
buy |
| m52575 | A ladder 10 ft long rests against a vertical wall. Let θ be the angle between the top of the ladder and the wall and let be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to θ when θ = π/3? |
buy |
| m52582 | A lattice point in the plane is a point with integer coordinates. Suppose that circles with radius are drawn using all lattice points as centers. Find the smallest value of such that any line with slope intersects some of these circles. |
buy |
| m52597 | A machinist is required to manufacture a circular metal disk with area 1000 cm2.
(a) What radius produces such a disk?
(b) If the machinist is allowed an error tolerance of ± 5 cm2 in the area of the disk, how close to the ideal radius in part (a) must the machinist control the radius?
(c) In terms of the ε, δ definition of limx→a f(x) = L, what is x? What is f(x)? What is a? What is L? What value of ε is given? What is the corresponding value of δ? |
buy |
| m52600 | A man starts walking north at 4 ft/s from a point P. Five minutes later a woman starts walking south at 5 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 min after the woman starts walking? |
buy |