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Solution: Given f(x,y)=ln √{x^2+y^2}, find (a) The direction and maximum rate of increase of f(x,y) at #10429
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[Solved] Find and identify the critical points of z=x^3+3xy^2-3x^2-3y^2+7 #10430
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[Solution] Find an identify the critical points of z=x^2-xy+y^3-x #10431
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[Solved] Find the maximum and minimum values of w=4x-(y)/(2)+(27z)/(2) on the surface x^4+y^4+z^4=1 #10432
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Solution: (a) Make a sketch of the region over which ∫_{0}^{π /2}{dx}∫_{0}^{ sin x}{dy} is b #10433
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(See Solution) (a) Make a sketch of the region over which ∫_{1/4}^{3/4}{dx}∫_{x^2}^x{(x+y)dy} is bein #10434
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(Solved) (a) Make a sketch of the solid in the first octant bounded by the plane x+y=1 and the parabolic cyli #10435
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(Solved) (a) Make a sketch of the solid bounded by the parabolic cylinders z+x^2=1, x+y^2=1, x-y^2=-1, and th #10436
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Solution: Find the area bounded by r=(1)/(√{1+θ )}, 0≤ θ ≤ π #10437
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[Solved] (a) Sketch the area bounded by the top half of the disc {{(x-1)}^2}+y^2=1 (b) Evaluate ∫_{D #10438
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[Solved] Find the volume of the solid based on the interior of the circle r= cos θ , and capped by the #10439
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[Solution] Find the volume of the solid based on the interior of the cardioid r=1+ cos θ and capped by #10440
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(See Solution) (a) Sketch the solid formed by the three coordinate planes and x+y+z=1 (b) Find the volume of this #10441
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[Solved] (a) Sketch the solid region in the first octant bounded by the elliptic cylinder 2x^2+y^2=1, and the #10442
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[Solution] Evaluate ∫{√{x^2+y^2}}dV over the region in the first octant bounded by x^2+y^2=2 #10443
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(Solved) (a) Sketch the solid region contained within the sphere x^2+y^2+z^2=16 and outside of the cone z=4-& #10444
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[Solved] Find the centroid of the solid region of uniform density between the xy-plane and the paraboloid #10445
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[Solved] Find the moment of inertia about the axis of a cone of uniform density D, of base radius a and heigh #10446
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Solution: Find the moment of inertia about a diameter of a spherical shell of uniform density D and bounded by #10447
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[Solved] Determine whether or not the following improper integral is convergent of divergent. If it is conver #10448
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[Solved] Evaluate the integral ∫_{D}{(x^2-y^2)dA} with D={ (x,y)| 0≤ x^2+y^2≤ 2, 0≤ xy&l #10449
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Solution: If F(x,y)=(3x^2y,2x-y), find ∫_{gamma }{vec{F}({x})d{x}} where γ is the directed pa #10450
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(Solved) (a) Parametrize the curve {{x}^{2/3}}+{{y}^{2/3}}={{a}^{2/3}} in the standard counterclockwise sense #10451
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[Solved] F(x,y) is define as F(x,y)=∫_{(2,π)}^{(x,y)}{[ -2u{v^2} sin (u^2v) ]du+[ cos (u^2v)-u^ #10452
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[Solved] Use Green’s Theorem to evaluate F(x,y)=( arctan y,-(xy^2)/(1+y^2)) around the curve 4x^2+9y^2 #10453
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(Solved) Compute the divergence and the curl of the vector function: F({x})=(x^2+y^2-xyz,xz^2 cos y,z^2{ #10454
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[Solution] A vector field is defined by F({x})=(y+z,x+y,x+z) (a) Find the Jacobian and determine if the f #10455
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Solution: (a) Parametrize the upper surface of the portion of the sphere x^2+y^2+z^2=4, contained within the #10456
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[Solution] (a) Sketch the surface z=x^2+4y^2 (b) Find a unit vector to the surface at the point (1, 0, 1) (c) #10463
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(See Solution) The position of a vector of a particle at time t is x(t)=(√{2} cos t, sin t, sin t) #10464
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Solution: (a) Find an classify all the critical points of f(x,y)=x^2+y^2+xy+x (b) Find the absolute maxi #10466
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[Solved] Let f(x,y)=(x+y)/(xy) (a) Find ∇ f (b) Find the directional derivative of f at (1, 1), in th #10467
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[Solved] Using spherical coordinates find the volume of the solid bounded below by the cone x^2+y^2=3z^2, and #10468
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[Solution] Find the area of that portion of the plane 2x+3y-z+7=0 inside the cylinder x^2+y^2=1. #10469
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(Solved) Let z=f(u,v) where u=x^2-y^2, and v=2xy. If {{z}_{uu}}+{{z}_{vv}}=0, show that {{z}_{xx}}+{{z}_{yy}} #10470
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(Solved) Find the point on the plane 2x-3y-4z=25 that is nearest to the point (3, 2, 1) #10471
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[Solution] Set up, but do not evaluate the iterated integral for the upper solid bounded by the surfaces #10472
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(See Solution) (a) Let C be a simple closed curve. Use Green’s theorem to show that the area bounded by C is given #10473
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Solution: Given the vectors x = (2, 0,-3) and y = (-1, 1, 2) find (a) |x| (b) The cosine of θ the angl #10474
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[Solved] Find the equation of the line joining the points: A(1, 2, 3) and B(-1, 2, 5) in (a) vector form. (b) #10475
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[Solution] Find the distance from the point (1, 2, 4) to the plane 2x + y + z = 12 #10482
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[Solution] A constant force F (1,-1, 5) acts through a point (-1, 3,-1). Find the resulting torque around the p #10483
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(See Solution) Determine whether the vectors (-3, 1, 1), (1,-2,-2) and (5,-1, 1) form a parallelepiped in R^3. If t #10485
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[Solution] Evaluate (a) ∫{(x)/(x^2+1)dx} (b) ∫{3x√{2x^2+5}}dx #10540
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Solution: Evaluate the following integrals, (a) ∫_1^8{√[3]{x}dx} (b) ∫_0^1{x^2{e^{x^3}}dx} #10542
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[Solution] Find the area between the curves y=-x^2+4x and y=x, form x = 0 to x = 3. #10543
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(See Solution) Suppose that we know the marginal profit at a production level x is given by MP(x)=5-(2000)/(x^2), x #10544
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[Solved] Suppose we know ∫_0^2{f(x)dx=8} and ∫_0^5{f(x)dx=11}. (a) What is ∫_2^5{f(x)dx} ? (b) Wh #10545
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(See Solution) Determine the absolute minimum and maximum of y=(x^2+4)/(x). on the interval [1, 5]. #10547
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(See Solution) Suppose you want to enclose 600 square yards with a rectangular fence and then divide the area in ha #10548
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(See Solution) Let f(x,y)=x^2y+3y^2-2xy^3+x-5, (a) Calculate (∂ f)/(∂ x) and (∂ f)/(∂ y). (b) C #10549
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Solution: Find the derivative of each of the following (a) y=x^4-5x^3+3x^2-4x+1 (b) f(x)=√[5]{x}+(1)/(x #10619
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Solution: Find the equation of the lines tangent and normal to the graph of f(x)=-x^3+3x^2-8x+8 at the point w #10620
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[Solved] Given that f(2)=3, f'(2)=8, g(3)=2 and g'(3)=4 (a) Find h'(2), where h(x)=(x^2+1)f(x) (b) Find h'( #10621
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(See Solution) A drug is injected into the bloodstream of a patient through her right arm. The concentration of the #10622
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[Solved] The total cost C(x) incurred by the On-Time Watch Company at one of its plants during a given day is #10623
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Solution: Use linear approximation to estimate √{50} #10625
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Solution: Find the first, second and third derivatives of f(x)=3x^4+12√{x}-(5)/(x^2) #10626
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(See Solution) Find the first and second derivative of g(x)=√{x^2+9} #10627
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[Solution] For g(x)=4x^3-x^4 (a) Determine the intervals on which the function is increasing and decreasing. ( #10628
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[Solved] A manufacturer can make a profit of $20 on each item if not more than 800 items are produced each we #10629
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[Solution] Use the linear approximation formula f({x_0}+Δ x)≈ f({x_0})+{f}'({x_0})Δ x to appr #10630
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(See Solution) Determine all intervals on which the function g(x)=(x^2)/(x-1) is increasing and decreasing. Then de #10632
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[Solution] Determine all intervals where the graph of f(x) = x^4-12x^3+ 48x^2-64x+11 is concave upward and conc #10633
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(See Solution) Find the absolute maximum and minimum values of h(x)=x+(9)/(x)+2 on the interval [1,10]. #10634
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[Solved] A rectangular garden of area 300 square feet is bounded on three sides by a brick wall costing $10.0 #10635
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Solution: Solve each of the following equations. a. {{125}^{2x-2}}={{25}^{3-x}} b. log_2(3x-1)=5 c. {{4} #10640
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[Solution] Differentiate each of the following: a. f(x)=x^3{e^{5x}} b. y=ln (x^4+3x^2+1) c. g(x)=(3ln x)/ #10641
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(See Solution) Find each of the following anti-derivatives: a. ∫{(2+x+12x^2+{e^x})dx} b. dx c. dx d. #10642
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[Solution] Evaluate each definite integral: a. ∫_1^6{x^2+(1)/(x)+{e^x}dx} b. #10643
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[Solved] Find the area under the graph of y=x^3-6x^2+9x+1 from x = 0 to x = 4. #10644
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(See Solution) a) Show that the Cobb-Douglas production function is homogeneous of degree (a+b) in labor and capita #10750
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[Solved] Write the Lagrangean and the first order conditions for the following problems and solve for X* and #10751
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(Solved) Find the antiderivative of the following functions (a) ∫{({e^x}-2{{ csc }^2}x-π)dx} (b) &in #10818
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[Solution] Find the definite integrals: (a) ∫_{0}^{π /4}{({{ sec }^2}x+1)dx} (b) ∫_{-1}^1{(x^3-2x- #10819
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(See Solution) Given the function f(x)=2x^2-7x+5, determine the following (a) ∫{(2x^2-7x+5)dx} (b) ∫_0^2{{ #10820
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[Solution] A projectile is moving on a horizontal plane with its acceleration given by the equation a(t)=2-3t. #10821
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[Solved] Given the function f(x)=5ln (x+1) (a) Estimate the area under the curve using Riemann curves (5 sub #10822
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[Solved] Find the limits of the following using L’Hospital Rule (a) {x→ 0} lim ({e^x}-1)/(x) (b) {x&rarr #10823
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[Solved] (a) A manufacturer wants to construct a Norman window with perimeter 30 ft. What are the dimensions #10824
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[Solved] Solve the following Cauchy-Euler equation x^2y''+2xy'-2y=2-ln (x^4) #10828
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Solution: Given that y_1= sin (x^2) is a solution of the equation xy''-y'+4x^3y=0 on the interval (0,&i #10829
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(Solved) What is the first and second derivative of f(x)=u(x) sin (x^2) ? #10830
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[Solution] Suppose that events E and F are independent. In addition, P(E) = 0.45 and P (F) = 0.2. What is P(E a #10911
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Solution: For the function given above, supply the following information: f(x)=(x^3-1)/(x^3+1) x-intercept(s #10992
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(See Solution) For the function given above, supply the following information: f(x)=(x^3-1)/(x^3+1) Discontinuiti #10995
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[Solution] For the function given above, supply the following information: f(x)=(x^3-1)/(x^3+1) Critical numb #10996
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[Solution] For the function given above, supply the following information: f(x)=(x^3-1)/(x^3+1) Intervals on #10997
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(Solved) For the function given above, supply the following information: f(x)=(x^3-1)/(x^3+1) Intervals on #10998
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[Solved] For the function given above, supply the following information: f(x)=(x^3-1)/(x^3+1) {f}''(x)= #11001
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(Solved) For the function given above, supply the following information: f(x)=(x^3-1)/(x^3+1) Intervals whe #11002
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[Solution] For the function given above, supply the following information: f(x)=(x^3-1)/(x^3+1) Intervals whe #11003
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[Solved] For the function given above, supply the following information: f(x)=(x^3-1)/(x^3+1) Inflection po #11004
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(See Solution) For the function given above, supply the following information: f(x)=(x^3-1)/(x^3+1) Sketch the gr #11005
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[Solved] Evaluate the definite integral by limit process ∫_1^3{(x^3+2x^2-3x+1)dx} #11006
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[Solution] Find both first partial derivatives z=y^3-4xy^2-1 #11093
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[Solution] Find both first partial derivatives z=ln √{xy} #11094
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(Solved) Find both first partial derivatives z=(xy)/(x^2+y^2) #11095
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[Solution] Evaluate {f_x} and {f_y} at the given point: f(x,y)= arccos xy at (1, 1) #11096
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[Solved] Find the first partial derivatives of w=(3xz)/(x+y) #11097
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[Solution] Find all the second derivatives z=x^4-3x^2y^2+y^4 #11098
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[Solved] Find all the second derivatives z= sin (x-2y) #11099
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