Find the volume of the described solid S. The base of S is the same base as in Exercise 58, but cross sections perpendicular to the x-axis are isosceles triangles with height equal to the base.
> Sketch the region enclosed by the given curves and find its area. y = у — Vx — 1, х — у— 1 y
> The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method. x? + (y – 1) = 1; about the y-axis
> The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method. y? – x² = 1, y = 2; about the y-axis
> The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method. y? – x? = 1, y = 2; about the x-axis
> The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method. у 3 —х? + 6х — 8, у — 0;B about the x-axis
> The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method. у — —х? + 6х - 8, у — 0;B about the y-axis
> Use a computer algebra system to find the exact volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x'sin x, y = 0, 0 <x< T; about x = -1
> Use a computer algebra system to find the exact volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y = sin?x, y = sin*x, 0 < x< T; about x = T/2
> Use a graph to estimate the x-coordinates of the points of intersection of the given curves. Then use this information and your calculator to estimate the volume of the solid obtained by rotating about the y-axis the region enclosed by these curves.
> Use a graph to estimate the x-coordinates of the points of intersection of the given curves. Then use this information and your calculator to estimate the volume of the solid obtained by rotating about the y-axis the region enclosed by these curves.
> Each integral represents the volume of a solid. Describe the solid. 27 (2 – x)(3* 2*) dx
> Sketch the region enclosed by the given curves and find its area. x = 2y?, x= 4 + y?
> Each integral represents the volume of a solid. Describe the solid. * y + 2 dy y?
> Each integral represents the volume of a solid. Describe the solid. 2ту Iny dy
> Each integral represents the volume of a solid. Describe the solid. | 2nx° dx
> If the region shown in the figure is rotated about the y-axis to form a solid, use the Midpoint Rule with n = 5 to estimate the volume of the solid. y 4 4 6 8 10 x 2. 2.
> Use the Midpoint Rule with n = 5 to estimate the volume obtained by rotating about the y-axis the region under the curve /
> (a) Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis. (b) Use your calculator to evaluate the integral correct to five decimal places. x? – y? = 7, x = 4; about y = 5
> (a) Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis. (b) Use your calculator to evaluate the integral correct to five decimal places. Vsin y, 0 < y < T, x = 0; about y
> (a) Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis. (b) Use your calculator to evaluate the integral correct to five decimal places. y = x, y= 2x/(1 + x³); about x =
> (a) Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis. (b) Use your calculator to evaluate the integral correct to five decimal places. у — сos'x, у — —-cos'x, —п/2 <х <
> (a) Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis. (b) Use your calculator to evaluate the integral correct to five decimal places. у 3 tan x, у — 0, х — п/4; аbout
> Sketch the region enclosed by the given curves and find its area. y = cos x, y=2 – cos x, 0<x<2n
> (a) Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis. (b) Use your calculator to evaluate the integral correct to five decimal places. у — хе ", у — 0, х — 2;B about th
> Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. x = 2y², x = y² + 1; about y = -2
> Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. x = 2y?, y > 0, x= 2; about y = 2
> Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. y = Vx, x = 2y; about x = 5
> Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. y = 4x – x', y = 3; about x = 1
> Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. у 3 4 — 2х, у — 0, х — 0; аbout x — —1
> Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. y = x', y = 8, x = 0; about x = 3
> Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. х+у — 4, х— у? — x + 4y + 4 =
> Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. x = 1 + (y – 2)?, x= 2
> Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. x = - Зу? + 12у — x = 0
> Sketch the region enclosed by the given curves and find its area. у3D sec*x, у—8 cos х, -T/3 < x< m/3
> Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. y = у — хУ, у — 8, х— 0 -3/2 у 3 8, х— 0 y
> Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. у — х, х— 0, у-2
> Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. ху — 1, х— 0, у —1, у—3
> Let V be the volume of the solid obtained by rotating about the y-axis the region bounded by / Find V both by slicing and by cylindrical shells. In both cases draw a diagram to explain your method.
> Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. у — х?, у—6х — 2х? y y
> Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. у — 4х — х*, у — х y y =x
> Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. y =e *? у —е*, у—0, х—0, х—1
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. х— 2Vy, х — 0, у — 9;B about the y-аxis
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. у —е", у — 0, х— —1, х— 1; about the x-axis
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. у — Vx — 1, у — 0, х — 5; about the x-axis
> Sketch the region enclosed by the given curves and find its area. y = x', y= 4x – x²
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. у — 1/х, у — 0, х— 1, х — 4; about the x-axis
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. у —х+ 1, у— 0, х — 0, х — 2; about the x-axis
> Find the volume of the described solid S. The solid S is bounded by circles that are perpendicular to the x-axis, intersect the x-axis, and have centers on the parabola / e/
> Find the volume of the described solid S. The base of S is the region enclosed by y = 2 - x2 and the x-axis. Cross-sections perpendicular to the y-axis are quarter-circles. y=2-x?
> Find the volume of the described solid S. The base of S is the region enclosed by the parabola y = 1 - x2 and the x-axis. Cross-sections perpendicular to the y-axis are squares.
> Find the volume of the described solid S. The base of S is the same base as in Exercise 56, but cross sections perpendicular to the x-axis are squares. Data from Exercise 56: Find the volume of the described solid S. The base of S is the triangular reg
> Find the volume of the described solid S. The base of S is the triangular region with vertices (0, 0), (1, 0), and (0, 1). Cross-sections perpendicular to the y-axis are equilateral triangles.
> Find the volume of the described solid S. The base of S is an elliptical region with boundary curve 9x2 + 4y2 = 36. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.
> Find the volume of the described solid S. The base of S is a circular disk with radius r. Parallel cross sections perpendicular to the base are squares.
> Sketch the region enclosed by the given curves and find its area. у — 12 — х?, у — х? — 6 y
> Find the volume of the described solid S. A tetrahedron with three mutually perpendicular faces and three mutually perpendicular edges with lengths 3 cm, 4 cm, and 5 cm
> Find the volume of the described solid S. a a a
> Find the volume of the described solid S. A pyramid with height h and rectangular base with dimensions b and 2b
> Find the volume of the described solid S. A frustum of a pyramid with square base of side b, square top of side a, and height h What happens if a = b? What happens if a = 0? a
> Find the volume of the described solid S. A cap of a sphere with radius r and height h
> Find the volume of the described solid S. A frustum of a right circular cone with height h, lower base radius R, and top radius r ード ーミー
> Find the volume of the described solid S. A right circular cone with height h and base radius r
> (a) A model for the shape of a bird’s egg is obtained by rotating about the x-axis the region under the graph of Use a CAS to find the volume of such an egg. (b) For a red-throated loon, a = 20.06, b = 0.04, c = 0.1, and d = 0.54. Graph
> (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 wit
> A log 10 m long is cut at 1-meter intervals and its cross- sectional areas A (at a distance x from the end of the log) are listed in the table. Use the Midpoint Rule with n = 5 to estimate the volume of the log. x (m) A (m²) x (m) A (m²) 0.68 0.53 1
> Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region. 4х + у? — 12, х—у
> A CAT scan produces equally spaced cross-sectional views of a human organ that provide information about the organ otherwise obtained only by surgery. Suppose that a CAT scan of a human liver shows cross-sections spaced 1.5 cm apart. The liver is 15 cm l
> Each integral represents the volume of a solid. Describe the solid.
> Each integral represents the volume of a solid. Describe the solid. " (o* – y") dy TT
> Each integral represents the volume of a solid. Describe the solid. "f', (1 – y°y° dy TT
> Each integral represents the volume of a solid. Describe the solid. [" sin x dx Jo
> Use a computer algebra system to find the exact volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y - x, y - xe' /2; about y = 3
> Use a computer algebra system to find the exact volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y = sin?x, y = 0, 0 < x< ™; about y = -1
> Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then use your calculator to find (approximately) the volume of the solid obtained by rotating about the x-axis the region bounded by these curves. у 31+
> Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then use your calculator to find (approximately) the volume of the solid obtained by rotating about the x-axis the region bounded by these curves. у — In
> Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places. (a)
> Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region. х —D1 - у?, х-- у? — 1
> Find the area of the shaded region. yA (1, е), y=e* y=xe**
> Compare a municipal bond with a tax-deferred annuity. When would one be more attractive than the other?
> Using the table in Example 14.13 on page 442 providing a comparison of tax- advantaged structures, explain why the qualified pension plan and the Roth IRA seem to be particularly attractive investments.
> Why is a qualified pension plan such an attractive tax shelter?
> Assuming that you didn’t regard a stock that declined since you bought it particularly highly, why wouldn’t you want to take a loss in the current year?
> Sarah had unrealized long-term capital gains and Marcy had unrealized long-term capital losses at year-end. When should each sell her shares: the current year or the next year?
> State how taxes are relevant in five major financial planning areas.
> When would a mutual fund be more attractive than an annuity?
> Which plan is more likely to be attractive to a younger person, a defined benefit or a defined contribution plan?
> Explain the difference between a defined benefit and a defined contribution plan.
> Explain the relationship of life cycle theory to retirement planning.
> When it came to investments, Richard and Monica could agree on only one thing—that they would have a tough time reaching a decision on asset allocations and individual investments. Previously, Monica had deferred to Richard on investment matters. Given R
> Ann was offered an annuity of $20,000 a year for the rest of her life. She was 55 at the time, and her life expectancy was 84. The investment would cost her $180,000. What would the return on her investment be?
> Todd was asked what he would pay for an investment that offered $1,500 a year for the next 40 years. He required an 11 percent return to make that investment. What should he bid?
> Marcy placed $3,000 each year into an investment returning 9 percent a year for her daughter’s college education. She started when her daughter was two. How much had she accumulated by her daughter’s 18th birthday?
> How many years would it take for a dollar to triple in value if it earns a 6 percent rate of return?
> Jason was promised $48,000 in 10 years if he would deposit $14,000 today. What would his compounded annual return be?
> What is the future value of an investment of $18,000 that will earn interest at 6 percent and fall due in seven years?
> What is the present value of a $20,000 sum to be given six years from now if the discount rate is 8 percent?
> Elena is in the 28 percent bracket and has the following real estate and non real-estate related costs. Nonmortgage interest and principal ……………………$ 4,000 Mortgage interest …………………………………………………15,000 Mortgage principal ………………………………………………….7,000 Real esta
> Given the following statistics, calculate the mortgage cost percent. Annual mortgage interest ……………………………………$ 9,000 Annual principal payment ……………………………………….2,000 Annual insurance and real estate taxes …………………..8,000 Yearly gross income …………………………………………
> How much would a person save by borrowing money at 6 percent for a home equity loan versus 18 percent for a credit card loan. Assume a marginal tax bracket of 30 percent.
> Monica continued to worry about the couple’s financial future. She began to question their investment in a home. She asked whether would be better to sell their home now and invest the proceeds. She estimated that the marketable securities would provide
