Suppose that f(x, y) = z²y. The directional derivative of f(x, y) in the directional (-1,-2) and at the point (z,y) = (1, 3) is

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Q: Suppose that the daily profit (in dollars) from the production and sale of x units of a product is…

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Q: Solve the differential equation. 2xy + 4x + (x² - 4) dy dx = 0 =

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Q: Determine the x-intercept of the plane: [x, y, z]= [3, 1, 3]+[1, 1, -1]+[0, 1, 3]

A: Question -   Determine the X intercept of the plane

Q: Find the arc length of y = 2x³/2 on 1 ≤ x ≤ 3.

A: y=2x321≤x≤3arc length(L)=∫ab1+(dydx)2dxd dx(xn)=nxn-1

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A: The given function is;  f(x)=sqrt(4-34x).

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Q: S Du Arriving at the eighth and penultimate gate, you immediately get to work. "Computer, translate…

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Q: Given (y)-16-²-², use the total differential to approximate or at (4.1) towards (24,1.05). Round…

A: △x=2.4-4=-1.6△y=1.05-1=0.05

Q: Change the Cartesian integral - ² dy dx into an equivalent polar integral. Then evaluate the polar…

A: To change the Cartesian integral ∫-55∫025-x2 dy dx into an equivalent polar integral. Then to…

Q: [5-A] [CLO 12] The line ℓ passes through the points (−3, −4) and (5, 1). Give an equation for the…

A: Given: The line l passes through the points -3,-4 and 5, 1. The objective is to find the equation…

Q: Write a rational function whose graph is shown below. -1 + 2 0 -2- T 1 1 + 2 F L 3 + 1 (4,0) 4 1 -10…

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Q: Find the volume of the solid generated by revolving the shaded region about the x-axis. 6 X₁ = 1, X₂…

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Q: [2-R] [CLO 13] On the Cartesian plane, sketch the solutions to 2x + 4y ≥ 8.

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Q: Find the volume of the solid obtained by rotating the region bounded by Y = 8x², x = :1, and y 0,…

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Q: has a point of inflection. 2 z = 2 3. r = 0, 4 4. # = 0, -4 g 5. r = 0, 1. Find all values of at…

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Q: Find the derivative of the function. f(0) = cos(0²) f'(0) = =

A: Given   f(thita) = Cos(thita2)

Q: Draw an accurate diagram of what follows and find resulting distance to the port: A ship sails on a…

A: Please see the below picture for detailed solution.

Q: Express the integrand as a sum of partial fractions and evaluate the integral. y² + 8y +49 (y² +49)²…

A: The given integral is:∫y2+8y+49y2+492 dy

Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 25 - x². What…

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Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: Find the extreme values of f(x,y) = xy subject to the constraint x² + y² -4 = 0. The extrema are…

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Q: Find the length of the curve (t) = (2 cos(3t), 2 sin(3t), 5t) for −8 ≤ t ≤ 8 Give your answer to two…

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Q: Sketch the region bounded by the given lines. Then express the region's area as an iterated double…

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Q: A cable runs along the wall from C to P at a cost of $7 per meter, and straight from P to M at a…

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Q: Let y = (x² + 5)5. Find the differential dy when x = 3 and dx = 0.5 - Find the differential dy when…

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Q: The perimeter of a rhombus is 68 inches and one of its diagonals measures 30 inches. Find the area…

A: Topic = Geometry

Q: a) Suppose that lim n-00 ∞ The series Enan n=1 an+1 an 1 == 2 converges ✓ by the ratio test <

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Q: Find the derivative of the function at the given point in the direction of A. f(x,y) = -6x-9y,…

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Q: Find the volume of the solid that lies under the elliptic paraboloid x/4 + y²19 21 and above the…

A: We have given paraboloid x24+y29+z=1 and rectangle [-1, 1]×[-2, 2]

Q: Find the exact length of the curve y = br (ex :/) 1) + لے سلاے ахо

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Q: Find the absolute extrema of the function, if they exist, over the indicated interval. Also indicate…

A: Given function is:fx=-0.001x2+4.2x-80We have to find the absolute extrema of the function.

Q: A volume is described as follows: 1. the base is the region bounded by x = y² + 8y + 50 and x = 2.…

A: A volume is described as follows: 1. The base is the region bounded by x=-y2+8y+50 and x=y2-22y+138.…

Q: Evaluate the limit sin 8x lim x 0 sin 2x

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Q: Find the equation for the tangent plane to the surface z = 9x² - 6y² at the point (2, 1, 30). OA.…

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Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

A: We have to find the volume of the solid by rotating the region in the firs qudrant bounded by the…

Q: Question 21 Suppose that is differentiable function and f'(r) 2 2r-1 for all are R. If f(0) = 1,…

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Q: Find the limit. lim 0-0 cos(0) 1 sin (0)

A: Given limit limθ→0cosθ - 1sinθ

Q: Find an equation of the tangent line to the curve at the point (1, -1-). y = x³e-x y =

A: To Find: Tangent line to y=x3e-x, at point 1, 1e

Q: Q18 Given s = 3a²c-2bc + 5abc² (a) (b) da dc || ||

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Q: Find the absolute extrema of the function, if they exist, over the indicated interval. Also indicate…

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Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by…

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Q: 10x3-8x4+2x3 2 2 X→0 15x4+3x3-5x Evaluate Lim

A: We need to find the given limit limx→010x43-8x34+2x2315x24+3x23-5x

Q: A function and the graph of a feasible region are given. f = -x + 5y 12 8 y (5,10), 4 8 (10,6) 12 x…

A: Maximum and minimum values of the function can occur at corner points.

Q: In this problem, p is in dollars and q is the number of units. Suppose that the demand for a product…

A: Given: Demand for product is given by 2p2q = 30000+9000p2, where p is in dollar and q is the number…

Q: Describe the given region in polar coordinates.

A: Please see the below picture for detailed solution.

Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

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Q: Given ƒ"(x) = 6x – 5 - and ƒ'(−2) = −1 and ƒ(−2) = 2. Find f'(x) = and find f(2)=

A: We need to find out the value of f'(x) and f(2) for which the second derivative is given.

Q: A tank contains 500 gallons of salt-free water. A brine containing 0.25 lb of salt per gallon runs…

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