Find the critical points for f(x,y)= 32xy-(x+y)^4 and classify them using the D-test as a local maximum, local minimum, saddle point, or none of these.

Q: Determine the directional derivative of f(x,y) = x³ + x cos(3y) at (1,0) in the direction of (3, 4).

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Q: Eliminate the parameter to find a Cartesian equation for the curve. x = 4 + 9 cos(t), y = 6 + 9…

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Q: Find the area of region A in Figure 6. G FIGURE 6 F:r = 16 cos 0, Tg = 1, F 2rx G:r = 1 rf = 8

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Q: 2. A particle is moving on the x-axis with a velocity of v(t) = t² - 3t-18. For what values of t> 0…

A: Given velocity function v( t ) = t2 - 3t - 18 For finding the interval in which velocity is…

Q: Find the gradient vector field of f(x, y) = xºy³ < V

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Q: Consider the following function. H(x, y)  =  7 ln(x3 + 2y2) (a) Find  fxx(2, 3) . (b) Find  fyy(2,…

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Q: The sum of three nonnegative numbers is 36, and one of the numbers is twice one of the other…

A: given sum of three nonnegative numbers is 36 one of the numbers is twice one of the other numbers…

Q: Find an antiderivative F(x) with F'(x) = f(x) = 5 + 24x³ + 21x6 and F (1) = 0. Remember to include a…

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Q: 2T Calculate L4 for f(x) = 57 cos (2) over [ 24, 2 L4= ←

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Q: 1. If the average value of the function fon the interval [a, b] is 15, then f f(x) dx = A. 15 b-a C.…

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Q: Use Separation of Variables to find the general solution. 30x² y³ y' - = 0 (Express numbers in exact…

A: We need to solve D.E. by using variable separation method.

Q: Consider the following function. h(u, v)  =  u3 + 18uv + 9v2 (a) Find the critical points of h.…

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Q: y

A: x1=2    , x2= 3 y1= -1 , y2=y   and distance between the points is 1

Q: 2. (a) Verify that all members of the family y = 2x³ + Cx-³ are solutions to the differential eq…

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Q: 6. Suppose that h(x) = g(f(x)) is a function where f(1) = 2 and f'(1) = 3, g(1) = 7, g'(1) = -4,…

A: Given thath(x)=g(f(x))f(1)=2, f'(1)=3, g(1)=7, g(2)=6, g'(2)=1We need to find tangent to h(x) at…

Q: Consider the series n=1 3 n+8 . Let sn be the n-th partial sum; that is,

A: Given that the series and s_n be the nth partial sum

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

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Q: Use method of undetermined coefficients 2X y" - 4y = 1 8xe

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Q: Let A(z) = f(t)dt, with f(x) shown in the graph below. sh da ch At what x values does A(x) have a…

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Q: A rectangle is constructed with its base on the x-axis and two of its vertices on the parabola y =…

A: Consider

Q: Given: 4n An -4n+ 11 For both of the following answer blanks, decide whether the given sequence or…

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Q: 3. Determine the coordinates on the unit circle for the following angles (given in radians). 0= 5.22…

A: Question number 3: Given: θ=5.22 radians We are required to find: The co-ordinates on the unit…

Q: A company determines that its weekly online​ sales, S(t)​,in hundreds of​ dollars, t weeks after…

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Q: 1. State Rolle's Theorem and draw a picture to illustrate it. 2. Which part of Rolle's Theorem is…

A: Rolle's Theorem states that if a function f is continuous on the closed interval [a,b] and…

Q: Find the zeros, if any, of the quadratic function using the quadratic formula. What are the…

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Q: Given F = (5yz, 5xz+ 2,5xy + 2z), find a function ƒ so that ₹ = Vƒ f(x,y,z) = + K Use your answer to…

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Q: a. Find the linear approximation for the following function at the given point. b. Use part (a) to…

A: fx,y=-x2+3y2 (a) Find the linear approximation of the function at the point 3,-2

Q: The interval of convergence of the power series (x+3) ² vistulos k=1 k (A) (-4,-2) (C) [-4, -2] 8…

A: We need to find interval of convergence.

Q: The marginal revenue from selling x cameras is 165 - 0.06x dollars per camera. Find the revenue…

A: given marginal revenue is 165-0.06x given R(0)=0

Q: 3 luate (x3 + 1)dx. -1 20

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Q: According to data from a medical association, the rate of change in the number of hospital…

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Q: Exercise (b) Write a formula that gives the amount of protein in a mixture of a pounds of alfalfa…

A: 25 pounds of alfalfa and 40 pounds of wheat mids, we have to find how many pounds of protein are in…

Q: Solve the triangle. If two possible triangles exist, solve both triangles and list information for…

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Q: Match the Taylor polynomial approximation of the function f(x) = e-x2/2 with its graph. (Select the…

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Q: Example 1 The function F(x) = x6 is an antiderivative of f(x) = x5 since F'(x) = f(x).

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Q: 9. In each part state the x-coordinates of the inflection points of f. Give reasons for your…

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Q: Identify the inflection points and local maxima and minima of the graphed function. Identify the…

A: Here we have to apply the application of differentiation.

Q: nswer 1. For the function f(x) = 5+5x-x', find the local extrema. Use the first derivative test to…

A: Please see the below pictures for detailed solution.

Q: Approximate the area under the curve y = x³ from x = 3 to x = 6 using a Right Endpoint approximation…

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Q: maur Textbook Question Chapter 8.2, Problem 18E The given curve is rotated about the y-axis. Find…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: V= V= [₁² f(x) dx 3

A: Given that the areas of the labeled region are

Q: Consider the following. f(x) = 7- 2²/12 Determine the value that the function f approaches as the…

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Q: Match the equivalent expressions. 5 = log₂ (x) 2= log(x) x = log₂ (5) x = log₂ (2) a 2t = 5 b 5² = x…

A: We know  if logay=x⇒y=ax

Q: Find the demand function for the marginal revenue function. Recall that if no items are sold,…

A: Here the marginal revenue function R'x=0.03x2-0.06x+162

Q: Let r(t) = Find f(t)dt ( )dt (don't include the +C) fF(t)dt = <[ Calculator 1 Check Answer

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Q: Find the surface area of the part of the plane z = [1, 5] × [0,5] = 2 + 4x + 3y that lies above the…

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Q: Use Separation of Variables to find the general solution. 3y': = x sec (y) (Express numbers in exact…

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Q: Find the indicated partial derivatives of: fx(x, y) = fy(x, y) = f(x, y) = 5x + 2y 7x - ly

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Q: Find the second derivative of f(x)=3x^(4)-5x^(3)+4x^(2)-x+8

A: given  f(x)=3x4-5x3+4x2-x+8 formula used (i) d dx(xn)=nxn-1(ii)  d dx(constant)=0

Q: Find the area of the region enclosed by f(x) and the​ x-axis for the given function over the…

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