Calculus Expert Answers & Study Resources

Use your calculator to approximate the integral using the method indicated, with n = 100. Round your answer to four decimal places. 20) dx (trapezoidal rule) A) 19.0349 B) 19.0855 C) 19.0870 D) 20.0855 21) dx (trapezoidal rule) A) 9.7873 B) 9.6718 C) 9.8093 D) 9.7516 22) dx (trapezoidal rule) A) 12.7991 B) 12.8501 C) 12.8227 D) 12.8473 23) dx (trapezoidal rule) A) 0.6520 B) 0.5982 C) 0.6363 D) 0.5980 24).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find values of x and y such that both fx(x, y) = 0 and fy(x, y) = 0. 1) f(x,y) = x3 - 4xy + 8y A) x = 0, y = 0 B) x = 2, y =.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the location of the indicated absolute extremum for the function. 1) Minimum A) x = -3 B) x = 3 C) x = 5 D) x = -5 2) Maximum A) No maximum B) x = 1 C) x = 4 D) x = -4 3).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the partial derivative. 1) Find fx(8, -4) when f(x,y) = 7x2 - 9xy. A) 160 B) -76 C) 148 D) 76 2) Find fy(-3, 1) when f(x, y) = 8xy - 9y. A) 0 B) -24 C) -33 D) 8 3) Find fx(-2, 3) when f(x,.

Find the Integral. 21) ∫(3x2)(4)√(10 + 2x3) A) (12/5)(10 + 2x3)5/4 + C B) (2/5)(10 + 2x3)5/4 + C C) - 2(10 + 2x3)-3/4 + C D) 3(10 + 2x3)5/4 + C 22) ∫(x6√(x7 + 3)dx) A) (1/14√(x7 + 3)) + C B) (2/21)x7(x7 + 3)3/2 + C C) (2/3)(x7 + 3)3/2 + C D) (2/21)(x7 + 3)3/2 + C 23).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the improper integral is convergent or divergent. 1) A) Convergent B) Divergent 2) A) Divergent B) Convergent 3) A) Divergent B) Convergent 4) A) Convergent B) Divergent 5) A) Divergent B) Convergent 6) A) Convergent B) Divergent 7) A) Convergent B) Divergent 8) A) Convergent B) Divergent 9) A) Convergent B) Divergent 10).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the percent of the area under a normal curve between the mean and the given number of standard deviations from the mean. 1) 3.01 A) 49.86% B) 99.87% C) 49.87% D) 50.13% 2) 2.41 A) 50.80% B) 49.20% C) 49.18% D) 99.20% 3) 1.64 A) 44.95% B) 94.95% C).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Assume x and y are functions of t. Evaluate dy/dt. 1) xy + x = 12; dx/dt = -3, x = 2, y = 5 A) -9 B) 3 C) 9 D) -3 2) x3 + y3 = 9; dx/dt = -3,.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the indicated relative minimum or maximum. 1) Minimum of f(x,y) = x2 + y2, subject to x + y = 1 A) f(0, 1) = (1/2) B) f(0, 1) = 1 C) f ((1/2), (1/2)) = (1/2) D) f ((1/2), (1/2)).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A die is rolled five times. Find the probability of getting the indicated result. 1) Two comes up zero times. A) 0.0001 B) 0.424 C) 0.161 D) 0.402 2) Two comes up one time. A) 0.116 B) 0.402 C) 0.003 D) 0.502 3) Two comes up two.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Evaluate dz. 1) z = -4x2 + 6xy + 2y2; x = 5, y = 4, dx = 0.02, dy = -0.03 A) -1.70 B) 1.70 C) 1.40 D) -1.40 2) z = (2x/y) + √(17xy); x = 10, y = 5, dx =.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean and standard deviation of the specified probability density function. 1) f(x) = (1/8) for [12, 20] A) μ = 15.5, σ = 2.28 B) μ = 16, σ = 2.31 C) μ = 1.6, σ = 2.29 D).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the median for the list of numbers. 1) 4, 4, 14, 25, 30, 42, 50 A) 30 B) 25 C) 24 D) 14 2) 16, 25, 30, 45, 65, 74, 85 A) 45 B) 65 C) 49 D) 30 3) 4, 3, 24, 13, 48, 35,.

Solve the problem. 31) Sales (in thousands) of a certain product are declining at a rate proportional to the amount of sales, with a decay constant of 6% per year. Write a differential equation to express the rate of sales decline. A) dy/dt = -0.06t B) dy/dt = -0.06y C) dy/dt = -0.94y D).

Find the x-value of all points where the function has relative extrema. Find the value(s) of any relative extrema. 19) f(x) = x2 + 2x - 3 A) Relative minimum of -2 at 0. B) Relative minimum of 0 at -2. C) Relative maximum of -4 at -1. D) Relative minimum of -4 at -1. 20).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Prepare a frequency distribution with a column for intervals and frequencies. 1) Use five intervals, starting with 0 - 4. 1 8 11 19 24 20 15 12 9 2 5 10 16 20 17 13 5 10.

Choose the graph that matches the equation. 16) z = -x2 - y2 A) B) C) D) 17) z = 3 - x2 A) B) C) D) 18) z = √(4 - x2 - y2) A) B) C) D) 19) z = 4x2 + 4y2 + 2 A) B) C) D) 20) z = 1.

Find the integral. 21) ∫((t3 + e5t)dt) A) (t4/4) + e5t + C B) (t2/2) + 5e5t + C C) (t4/4) + (e6t/6) + C D) (t4/4) + (e5t/5) + C 22) ∫(72xdx) A) (72x/2) + C B) (73x/3) + C C) (72x/ln7) + C D) (72x/2ln7) + C 23) ∫((9x-5 - 4x-1)dx) A) (9/5)x-4 - 4ln|x|+ C B) - (9/4)x-4 - 4ln|x|+.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use integration by parts to find the integral. 1) ∫(2xexdx) A) xex - 2ex + C B) 2ex - ex + C C) 2ex - 2xex + C D) 2xex - 2ex + C 2) ∫(e2xx2dx) A) (1/2)x2e2x - (1/2)xe2x + C B) (1/2)x2e2x.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the integral. 1) ∫(x3)dx A) 4x4 + C B) (x2/3) + C C) 3x2 + C D) (x4/4) + C 2) ∫(4x2/3)dx A) (4/3)x5/3 + C B) (8/3)x5/3 + C C) (12/5)x5/3 + C D) 6x5/3 + C 3) ∫(30)dx A) 0 B) 30 + C C) 15x2 D) 30x.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find any inflection points given the equation. 1) f(x) = 5x2 + 10x A) Inflection point at (-2,-10) B) No inflection points C) Inflection point at (-1,-5) D) Inflection point at (2,-10) 2) f(x) = 2x3 + 15x2 + 24x A) No inflection.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Evaluate the integral. 1) A) (136/3)y B) 44y C) 4x(4x - 5) D) 27 2) A) (e4x+5 - e4x+3/4) B) (e20+y - e12+y/4) C) 4(e20 +y - e12+y) D) e4x+5 - e4x+3 3) A) (1/6)[(36 +y)3/2 - (18 + y)3/2] B) (2/3)[(36 +y)3/2 - (18 +.

Find the area between the graph of the function and the x-axis over the given interval, if possible. 30) f(x) = (11/(x - 1)2) for (-∞, 0] A) 11 B) 1 C) -11 D) Divergent 31) f(x) = (3/(x - 1)3) for (-∞, 0] A) -1.5 B) -0.5 C) 1.5 D) Divergent 32) f(x) = 6e-x for (-∞, e] A) -0.396 B) 0.396 C) -90.924 D).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find fx(x, y). 1) f(x, y) = (1/√(x2 + y2)) A) - ((1/2(x2 + y2)3/2)) B) - ((x/2(x2 + y2)3/2)) C) ((y/(x2 + y2)3/2)) D) - ((x/(x2 + y2)3/2)) 2) f(x, y) = ln((y9/x8)) A) - (8/x) B) - (8y9/x) C) -ln((8y9/x9)) D) -ln((8/x)) 3) f(x,.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by the curves. 1) y = x + 1, y = 0, x = -1, x = 6 A) 49π B) (343/3)π C).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find f"(x) for the function. 1) f(x) = 6x2 + 6x - 2 A) 12x + 6 B) 6 C) 12 D) 0 2) f(x) = 3x4 - 5x2 + 4 A) 12x2 - 10x B) 12x2 - 10 C) 36x2 - 10 D) 36x2 -.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Evaluate the definite integral. 1) A) 12 B) 18 C) 6 D) 9 2) A) - (13/2)√(13) B) -√(13) C) - (17/2)√(13) D) - (17/2) + 2√(13) 3) A) 14.5 B) 17.5 C) -22.5 D) 22.5 4) A) - (2/3) B) 0 C) - (8/3) D) (8/3) 5) dx A) (10/3) B) 0 C) 3 D) -2 6).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The function represents the rate of flow of money in dollars per year. Assume a 10-year period and find the present value. 1) f(x) = 500 at 2% compounded continuously A) $45,468.27 B) $4531.73 C) $5535.07 D) $20,468.27 2) f(x) = 2000.

Find the volume under the surface z = f(x,y) and above the rectangle with the given boundaries. 30) z = 6x2y; 0 ≤ x ≤ 4, 0 ≤ y ≤ 3 A) 1256 B) 676 C) 2256 D) 576 31) z = x2 + y2; 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 A) (4/3) B).

Use the definite integral to find the area between the x-axis and f(x) over the indicated interval. 31) f(x) = x2 - 6x + 9; [2, 4] A) (1/3) B) (2/3) C) (7/3) D) (4/3) 32) f(x) = 2x - x2; [0, 2] A) (5/3) B) (4/3) C) (7/3) D) (2/3) 33) f(x) = (3/x3); [1, 3] A) (1/3) B) 3 C) (4/3) D) (1/2) 34).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Decide whether or not the function is a probability density function on the indicated interval. 1) f(x) = (3/98)x2; [3, 5] A) Yes B) No 2) f(x) = (4/81)x3; [0, 3] A) Yes B) No 3) f(x) = (1/3)x - (1/6); [3, 4] A).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Approximate the area under the graph of f(x) and above the x-axis using n rectangles. 1) f(x) = 2x + 3 from x = 0 to x = 2; n = 4; use right endpoints A) 15 B) 13 C).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the Integral. 1) ∫(4(2x + 5)3dx) A) (3/8)(2x + 5)4 + C B) (1/2)(2x + 5)4 + C C) (3/4)(2x + 5)4 + C D) (1/4)(2x + 5)4 + C 2) ∫(3(2t + 5)3dt) A) (3/8)(2t + 5)4 + C B) (1/2)(2t +.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the general solution for the differential equation. 1) (dy/dx) = 12x2 A) y = 12x3 + C B) y = 4x3 + C C) y = x3 + C D) y = (x3/3) + C 2) (dy/dx) = x - 24 A).

Solve the problem. 63) A company's cost for operating two warehouses is C(x, y) = 6x2 + 4x + 12y2 + 8y + 9, where x is the number of units in warehouse A and y is the number in B. Find the average cost to store a unit if A.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use n = 4 to approximate the value of the integral by the trapezoidal rule. 1) A) (9/4) B) (45/8) C) (9/2) D) 9 2) A) (55/2) B) 88 C) 44 D) 22 3) A) (32/3) B) 11 C) 15 D) 22 4) A) (987/400) B) (987/200) C) (497/100) D) (987/100) 5) A).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the table of ∫s or a computer or calculator with symbolic integration capabilities to find the interal. 1) ∫((4xdx/x2(1 + 4x2))) A) ln|(1 + 4x2/x2)|+ C B) ln|(x2/1 + 3x2)|+ C C) - 3ln|(1 + 3x2/x2)|+ C D) - 2ln|(1.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. Use the normal curve approximation to the binomial distribution. 1) Estimate the probability of getting exactly 43 boys in 90 births. A) 0.0729 B) 0.1628 C) 0.0764 D) 0.0159 2) A multiple choice test consists of 60 questions. Each.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Find two numbers whose sum is 320 and whose product is as large as possible. A) 10 and 310 B) 160 and 160 C) 159 and 161 D) 1 and 319 2) Find two numbers x and y.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Assume the distribution is normal. Use the area of the normal curve to answer the question. Round to the nearest whole percent. 1) A machine produces bolts with an average diameter of 0.30 inch and a standard.

Find dy/dx by implicit differentiation. 21) xy + x = 2 A) - (1 + y/x) B) (1 + x/y) C) (1 + y/x) D) - (1 + x/y) 22) xy + x + y = x2y2 A) (2xy2 - y - 1/-2x2y + x + 1) B) (2xy2 - y/2x2y + x) C) (2xy2 + y/2x2y - x) D).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the area between the curves. 1) y = 2x - x2, y = 2x - 4 A) (37/3) B) (32/3) C) (31/3) D) (34/3) 2) y = x2 - 5x + 4, y = -(x - 1)2 A) (8/7) B) (9/8) C) (8/9) D) (7/8) 3).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the expected value of the probability density function to the nearest hundredth. 1) f(x) = (1/3); [3, 6] A) 4.50 B) 4.00 C) 5.00 D) 4.17 2) f(x) = (1/5); [0, 5] A) 2.50 B) 5.00 C) 2.40 D) 12.50 3) f(x) = (x/8) - (1/4);.

Graph the function on the indicated domain, and use the capabilities of your calculator to find the location and value of the indicated absolute extremum. 20) f(x) = (x - 8)(x + 3); [0, ∞) Minimum A) -30.25 at x = 2.5 B) -30.21 at x = 2.7 C) -30.16 at x = 2.2 D) -29.89.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Evaluate the function. 1) Find f(5, 1) when f(x, y) = 7x + 3y - 3. A) 38 B) 28 C) 35 D) 32 2) Find g(-2, -1) when g(x, y) = 6y2 - 7xy. A) 9 B) 10 C) -8 D) -6 3) Find h(3, 6).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Sketch the graph and show all extrema, inflection points, and asymptotes where applicable. 1) f(x) = 2x3 - 3x2 - 12x A) Rel min: (3, -30) No inflection points B) Rel max: (0, 0), Rel min: (-2, 8) Inflection point: (-1, 4) C) No.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the range for the set of numbers. 1) 6, 19, 2, 13, 12 A) 6 B) 17 C) 19 D) 2 2) 22, 39, 42, 58 A) 39 B) 58 C) 17 D) 19 3) 110, 468, 143, 655, 31, 270 A) 127 B) 110 C) 545 D) 468 4) 70,.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Find the approximate number of batches (to the nearest whole number) of an item that should be produced annually if 160,000 units are to be made. It costs $2 to store a unit.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find dy for the given values of x and Δx. 1) y = x3 + 2x; x = 2, Δx = 0.01 A) 0.14 B) 0.07 C) 0.007 D) 0.014 2) y = (1/x); x = 10, Δx = -0.003 A) 0.0003 B) 0.03 C).

Use the standard normal curve table to find the z-score for the given condition. 21) 4.01% of the total area is to the left of z. A) -1.74 B) 1.70 C) -1.75 D) -1.76 22) 4.01% of the total area is to the right of z. A) -1.75 B) 1.75 C) 1.74 D) 1.76 23) 20.05% of the total area is.