(a) Find the partial derivative of f with respect to x. fx(X, y) = (b) Find the partial derivative of f with respect to y. fy(x, y) =
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Q: needed to be solved correclty in 15 minutes and get the thumbs up please show neat and clean work…
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Q: 11. Find the first four nonzero terms in a power series expansion of the solution to the given…
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Q: 5. Solve the initial value problem. dx 3x 7x Зху dy 0, y(1)= 3
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A: Please see the below picture for detailed solution.
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- Find the derivative of the function at Po in the direction of A. f(x,у) 3 4ху + 3у?, Po(3,0), А-D -3і - 4] (PA) (3,0) (Type an exact answer, using radicals as needed.)please help!17. Sketch the ioiicwing curve by cing seconá derivative: 1) y= 1+x 2) y=-x(x-7) 3) y (x+ 2) (x-3) 4) y=x(5-x) (ans.: max.(1,0.5); min.(-1,-0.5)) (ans.: max.(7,0); min.(2.3,-50.8)) (ans.: max.(-2,0); min.(1.3,-18.5)) (uns. mux.(3.5,18.5);ra0,0)) 18. What is the smallest perimeter possible for a rectangle of area 16 in.2 ? (ans.: 16) 19. Find the area of the largest rectangle with lower base on the x- axis and upper vertices on the parabola y 12-x. (ans.:32) 20) A rectangular plot is to be bounded on one side by a straight river and enclosed on the other three sides by a fence. With 800 m. of fence at your disposal. What is the largest area you can enclose ? (ans.:80000) 21) Show that the rectangle that has maximum area for a given perimeter is a square. 22) A wire of length L is available for makıng a circie and a square. How should the wire be divided between the two shapes to maximize the sum of the enclosed areas? (ans.: all bent into a circle) 23) A closed container is made from a…
- The temperature on a cubic box [0, 4] × [0, 4] × [0, 4] (measured in meters) can be describedby the function T (x, y, z) = x2y + y2z degrees F◦. A fly is in position (1, 2, 1) and takesoff in a straight line to the corner (4, 0, 4). Use directional derivatives to calculate the changein temperature the fly experiences as she takes off. Give your answer with 2 decimal digitscorrect.This question is about gradients and directional derivatives. How can you tell the differences between these questions? Type 1: given that phi = x^2y^2z^2, find grad phi, grad phi at (-1,1,1) and a unit vector in this direction, the derivative of phi at (2,1,-1) in the direction of i and d = 3/5i + 4/5kThis question requires you to first find grad phi, plug in the coordinates and make a unit vector out of it, then multiply this unit vector by the two directions to get two solutions. Type 2: calculate the directional derivative of lamba(x) = x^2yz + 2xz^2 at the point (1,-2,1) in the direction of vector v=1/3(1,1,2) While, at first, it looks similar to the previous question, the working out is different. It requires you to find grad phi and sub in (1,-2,1). Then, you find the magnitude of the vector. You multiply grad phi at (1,-2,1) by the vector and divide all of that by the magnitude to give you the answer. I don't understand why it's different, Type 3: consider the scalar field phi…