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[Solved] Find the volume of a pyramid of height 160 feet that has a square base of side 300 feet. These dimen #26657
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(Solved) A dome “twice as big” as that of exercise 9 (see text) has outline y=120-x^2/(120) for -120≤ #26658
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[Solved] A pottery jar has circular cross sections of radius 4- sin x/(2) inches for 0≤ x≤ 2pi . S #26659
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(See Solution) Compute the volume of the solid formed by revolving the region bounded by y=x^2,y=4-x^2 about (a) th #26661
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[Solved] Compute the volume of the solid formed by revolving the region bounded by y=x^2 and x=y^2 about (a) #26662
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[Solution] Let R be the region bounded by y=x^2 and y = 4. Compute the volume of the solid formed by revolving #26663
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Solution: Suppose that the circle x^2+y^2=1 is revolved about the y-axis. Show that the volume of the resultin #26664
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[Solution] Sketch the region, draw in a typical shell, identify the radius and height of the shell, and compute #26665
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(Solved) Sketch the region, draw in a typical shell, identify the radius and height of the shell, and compute #26666
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[Solved] Sketch the region, draw in a typical shell, identify the radius and height of the shell, and compute #26667
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[Solution] Use cylindrical shells to compute the volume of the region bounded by x=y^2 and x = 4, revolved abou #26668
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[Solution] Use the best method available to find the volume of the region bounded by y=2-x^2,y=x (x>0) and the #26669
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(See Solution) Use the best method available to find the volume of the region bounded by y={e^x}-1,y=2-x and the x- #26670
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[Solved] Use the best method available to find the volume of the region bounded by y= sin x and y=x^2 revolv #26672
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[Solution] Approximate the length of the curve using n secant lines for n = 2; n = 4. y=ln x,1≤ x≤ 3 #26673
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Solution: Compute the arc length exactly. y=2ln (4-x^2),0≤ x≤ 1 #26674
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[Solution] Set up the integral for the surface area of the surface of revolution, and approximate the integral #26675
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Solution: Set up the integral for the surface area of the surface of revolution, and approximate the integral #26676
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[Solved] Set up the integral for the surface area of the surface of revolution, and approximate the integral #26677
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[Solved] Identify a function f and a point (a, f (a)), for which the difference quotient (frac{3)/(7+x) #26693
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[Solution] Show that if R(x)=6x and C(x)=x({{(x-3)}^2}+6) are your revenue and cost functions, then your operat #26705
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[Solution] What value of a make f(x)=x^2+(a)/(x) have a (a) local minimum at x = 2? (b) point of inflection a #26716
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(Solved) Let g be a differentiable function whose values and derivatives for selected t are given by the tabl #26727
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(Solved) Find the slopes of the figure-eight-shaped curve y^4=y^2-x^2 at the points ((√{3})/(4),1/2) an #26738
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(Solved) A spherical lollipop in your mouth is giving up volume at a steady rate of 0.08 inL/min. How fast wi #26749
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[Solved] Near its intersection with East-West Highway, Wisconsin Avenue can modeled by the equations y= #26760
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[Solved] A rectangular box with an open top is to have a volume of 10 cubic feet. The length of the base is t #26767
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Solution: Compute the following and simplify (a) Compute and simplify: (d)/(dx)((x)/(√{x^2+2)}) #26769
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[Solution] (10 points each) (a) Find the equation of the tangent line at (x, y) = (1, 1) when x^2+y^3=1+xy^2. ( #26770
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(See Solution) Consider the function whose graph is shown (right). Consider also its derivative and its second deri #26772
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[Solved] Suppose you invest in a scheme whose future value after t years is given by F={e^{0.01t+0.005{t^2}}} #26773
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[Solution] Find δ in terms of ε for {x→ 1} lim (x^2-x+1)=1 #27075
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[Solution] Evaluate ∫_0^1{x^2{e^{3x}}dx} #27076
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(Solved) Estimate the error using the indicated partial sum {{S}_{80}}, ∑limits_{k=1}^{&infi #27077
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[Solution] Estimate the error using the indicated partial sum {{S}_{200}}, ∑limits_{k=1}^{&inf #27078
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Solution: Consider the spherical tank below. If the tank is full of water, how much work is required to pump t #27079
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[Solved] Solve the same problem as above if the tank is two thirds full of oil that a density of 900 kg m3 . #27080
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(Solved) Consider the spherical tank below. If the tank is full of water, how much work is required to pump t #27081
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(Solved) Solve the same problem as above if the tank is two thirds full of oil that a density of 900 kg m3 . #27083
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[Solved] Find a rectangular equation of the portion of the cycloid given by the parametric equations x = a(t #27197
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[Solution] Find a rectangular equation of the portion of the cycloid given by the parametric equations x = a(t #27198
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[Solution] Solve the following differential equation: ( cos x+y)dx=dy #27199
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(See Solution) How much work is needed to empty a tank by pumping water through the top of a full rectangular tank #27200
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[Solution] Calculate ∫_{(√{3})/(2)+1}^2{√{2x-x^2}dx} #27201
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Solution: Evaluate: {x→ ∞ } lim (√{x^2+3x}-x) #27203
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(Solved) Expand: (2x+1)/(1-x^2) #27204
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(See Solution) Find the equation in polar coordinates for the curve: x={e^{2t}} cos t , y={e #27205
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Solution: Find the solutions of each of the following equations dy/dx- 2y = ex y(0) = 0 #27219
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[Solved] Find the solutions of each of the following equations dy/dx= x + y y(0) = 2 #27220
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Solution: Find the solutions of each of the following equations xdy/dx= tan x - y #27221
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[Solved] Find the solutions of each of the following equations (x + x2) dy/dx+ xy = 1 + x #27222
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(See Solution) Find the solutions of each of the following equations dy/dx-2y/x= 1 #27223
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[Solution] Find the solution of each of the following equations. (ex + 2xey) dx + x^2ey dy = 0 #27225
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(See Solution) Find the solution of each of the following equations. (sin y - sin x) dx + (1 + x) cos y dy = 0 y(0) #27226
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(Solved) Find the solution of each of the following equations. (?y - 2x) dx +((x + 1)/(2?y))dy = 0 y(0) = 1 #27227
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(See Solution) Find the solution of each of the following equations. (2x + y) dx = (2y - x) dy #27228
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(Solved) Find the solution of each of the following equations. (dy)/(dx)=(1-2x+2y)/(2y-2x) #27229
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(See Solution) Blood carries a drug into an organ at a rate of 3 cm3/sec and leaves at the same rate. The organ has #27230
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[Solved] A 1 liter tank is filled with a salt solution containing 4 grams of dissolved salt. At t = 0, a hole #27231
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[Solved] At t = 0, 1 mole of chemical A and 1 mole of chemical B are dissolved in a liter of water. Eventuall #27232
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(See Solution) A cup of coffee is heated to 100 degrees Centigrade at t = 0 minutes. The cup is placed in a refrige #27233
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(See Solution) An object of 5 kg is released from rest 1000 meters above the ground level and allowed to fall under #27234
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[Solved] Introduction to Differential Equations. Separation of Variables. dy/dx= 1 + y2 #27236
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[Solved] Introduction to Differential Equations. Separation of Variables. dy/dx+ 7y = 0 #27237
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[Solved] Introduction to Differential Equations. Separation of Variables. dy/dx=y(y + 1)/x #27238
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[Solution] Introduction to Differential Equations. Separation of Variables. ydy/dx= x + xy2 y(0) = 2 #27239
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(See Solution) Introduction to Differential Equations. Separation of Variables. dy/dx+ xy = x y(0) = 2 #27240
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[Solution] Integration ?x^2 ln x dx #27241
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(See Solution) Integration ?x cosh x dx #27242
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(See Solution) Integration ? ?4 - x^2 dx #27243
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[Solution] Integration ?x + 4/x + 2dx #27244
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[Solved] Integration ?8x^2/(x2 + 1)(x- 1)dx #27245
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Solution: Special Integrating Factors, Substitutions and Transformations x2 dy/dx= y2 + xy Hint: Try v =y/x #27247
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(Solved) Special Integrating Factors, Substitutions and Transformations (ex + y) dx + x dy = 0 #27248
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Solution: (Special Integrating Factors, Substitutions and Transformations (e^{2x} - y^3)dx + 3y^2 dy = 0, y(0) = 0 #27249
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(See Solution) Special Integrating Factors, Substitutions and Transformations (2xy - 1) dx +x/ydy = 0 #27250
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[Solved] Special Integrating Factors, Substitutions and Transformations (1/y+ x)dx =1/y2 dy #27251
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[Solution] (a) Part of a landscape generated in a computer game is defined by the quadric surface z=3x^2+2xy+y #27254
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[Solution] (a) The point (2, 1, 0) is rotated through 180° abou #27255
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(See Solution) (a) The vertices of a parallelogram plane segment are A(3, 4, 1), B(0, 1, 4), C(2, 0, 3)andD(5, 3 #27256
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Solution: B1. (a) Solve the second order ordinary differential equation ({d^2}x)/(d{t^2)}+(dx)/(dt)-2x=2t, g #27258
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[Solution] (a) A smooth sphere A of mass 6 kg, moving with speed 5 ms^{-1} on a smooth horizontal surface #27259
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[Solution] (a) Consider the first order ODE (dy)/(dx)={e^{-4x}}-3y, y(0)=1. (i) #27260
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[Solved] The forthcoming zombie apocalypse can be modeled with the differential equation (dP)/(dt)=kP. On the #27580
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(Solved) aDoes the graph of a function f(x)=(4{x^7}+3x-4)/(9{x^7)-1003} have a horizontal asymptote? If it do #27749
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[Solution] Find lim (x^4-x^2+x+3)/(x^3+1), when x→ 1 #27750
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[Solved] Find the derivative of f(x)={e^{2x-5}}(x+3) #27751
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[Solution] Find the derivative of f(x)=x^2+x-3 using the definition of the derivative #27752
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(Solved) Find the antiderivative of f(x)={e^x}+x^2+x #27753
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(Solved) Find the antiderivative of f(x)=-{e^{-x}}+x #27754
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(See Solution) Find the area under the curve given by the function f(x)=x^3+x^2-1 on the interval [-2,1] #27756
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[Solution] Determine the value of r, if any, such that y=e^rx is a solution of the differential equations given #27829
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[Solved] Use Euler's method with the given step size (?x or ?t) to approximate the solution of the initial va #27830
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[Solution] A tank with a 1000-gal capacity initially contains 500gal of water that is polluted with 50lbs of pa #27831
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[Solved] Polonium-210 is a radioactive element with a half life of 140days. Assume that 20 milligrams of the #27832
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(See Solution) Determine whether the following sequences are (eventually) decreasing, (eventually) increasing, or n #27834
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[Solution] Evaluate the limit (if it exists) of each of the following sequences. Indicate the results (definiti #27835
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(See Solution) A bored student enters the number 0.5 in her calculator, and then repeatedly computes the square roo #27836
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[Solution] Give an example of 2 sequences { {a_n} } and { {b_n} } such that; a - { {a_n} } and { {b_n} } are di #27837
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[Solved] Find the sum of each of the convergent series given below a- ∑limits_{k=1}^{∞ }{((1)/({{2) #27838
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[Solved] Determine whether each of the series below is divergent, absolutely convergent (hence convergent) or #27839
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[Solved] Use an appropriate Taylor polynomial of degree 2 to approximate tan 61deg #27840
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