Please help me understand and the steps taken in the process. Thank you Given Find the following. a) fx b) fy f(x,y)=x3y2-3xy.

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A: Given  v = pi r^2 h = 45 h = 45/(pi r^2)   the metal used is just the surface area a = 2*pi r^2 + 2…

Q: Question a) b) Let f(x, y) = 2√x - y²e-2xy Find fx and fy. Evaluate fxxy(4,-1). + NIA

A: Given :fx,y=2x-y2e-2xy+2y

Q: z = (x + y)², x = s²t, y = st². Use the Chain rule to find dz ds for t= 1 and s = 2.

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Q: Find the following Wronskian: W(4, 3t, e-³¹, te-³1) O-972e-6t 0-972e6t 6 972e6t O 972e-6t 00 O-6

A: We can find the Wronskian .

Q: Part c: ( 1. Find the gradient of the function f(x, y, z) = ln(xy) - zx² at the point (1, 1, -1). 2.…

A: We have to find the gradient and directional derivative.

Q: 5. (x² + y² + 1)dx - 2xydy = 0

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Q: Determine any planes that are parallel or identical. (Select all that apply.) OP₁: -60x + 90y + 120z…

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Q: For the curve f(x) = Find the horizontal and vertical asymptotes. x-4x² +2 x² - 4x +4

A: This question can be solved using the concept of horizontal and vertical asymptote of rational…

Q: Match the functions in Column A with their corresponding antiderivatives in Column B. Column A a.…

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Q: Suppose that the concentration (measured in gm3) of nitrogen in the soil along a transect of land…

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Q: Let f: [1,1]→ R be a function given by f(x)=2x-x2. Then the inverse image (preimage) of [0,4] under…

A: The answer is option D

Q: 4 Use the substitution z +9=u² to evaluate √√+9

A: Note: Since, the student has asked to solve only question no. 4, so we are solving accordingly…

Q: The parametric equations of the line that passes through A(-3,5,9) and B(-4,-7,2) is: x=-3-t,…

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Q: (z In z + 5)dz

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Q: 4. (x² + y²)dx − 2xydy = 0

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Q: x+3y=x².

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Q: uring Runge-Kutta Method of fourth order, salve dy + y + xy² = 0, $ (0) = 1 by taking h= 0.1 لا

A: Runge Kutta Method of fourth order :-dydx= f(x,y)   , yo = xoyn+1=yn+16(k1+2k2+2k3+k4)where k1= h…

Q: Suppose f'(x) = x² - 1. Then the graph of f is concave upward on 0 (-∞0,0) O (-1,1) (0,00) O (-∞,…

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Q: Given the matrices A - 5 -5 2 2 2 - 2 and B - 4 2 -1 -2 5 0 A. It is Select an answer to multiply…

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Q: A B - f sin(1-x) (2 cos(1-x))4 dx (2-sin(1-x)5+C 5 (2-cos(1-x)5+C 5 O A OB O O D OE None of the…

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Q: Evaluate (In x)³ dx

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Q: Ja Inadr

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Q: Evaluate (x² - 1)³² dr.

A: Our Aim is to evaluate the integral given below:-∫x2-12 dx -(i)

Q: π/2 The integral f/2 So sin drde is equal to cos 0 O-1/2 O 1/2 0 1 00 10

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Q: If f(x, y) = √6xy - 4x + 30y then fa = Select one: O True O False -4√6xy+3y √6xy

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Q: √x +3 If f(x, y) = xy +7 the domain of f(x, y). Select one: True O False then the point (1, −7) is…

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Q: 2. Solve the following 4th order linear differential equations using undetermined coefficients: y…

A: We need to solve D.E.

Q: Một chuyển động có phương trình: R(t) = (cos(4t))i + (sin(4t))j + 4tk. Tìm vector tiếp tuyến đơn vị…

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Q: If then fyy = Select one: O True O False f(x, y) = 2(x² + x) (x - y)³ x² + y x - y

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Q: Question a) b Let f(x, y) = x³-4xy² x²-2y Find the first partial derivatives of f. Determine whether…

A: According to question,Given Function,fx, y = x5 -4xy2x2 - 2y

Q: If  f(x) = 4/x and g(x) = 6/x, find f(g(x)) and g(f(x))

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Q: EV None of the choices Ocot³ (1)-cot (1) - ○tan³ () - tan() Ocot³ (¹)-tan (1)

A: givenI=∫cot4(1θ)θ2dθlet  1θ=x-1θ2=dxdθ1θ2dθ=-dxI=-∫cot4(x)dx…

Q: The following limit Select one: O O equals 16 3 equals 0. None of them O does not exist. O equals 3…

A: This question is based on two variable limits.

Q: If f(x, y) = ln (xy) — 5 sin y, then ƒx(1, ´) = T Select one: True O False

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Q: If f(x, y) = A In (x² - y) -x+y+1 O {(x, y) x² > y, {(x,y)|x² ≥ y, ○ ○ {(x, y) x² > y, | then the…

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Q: 5. The angle between the tangent line and the normal line is (a) 180° (b) 90° (c) 45° 6. If x= 3t-2…

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Q: Solving the following secondary order differential equation: d²x dx dt² 3. +2x = 5e-³t dt

A: Solve differential equation

Q: Which of the following is the partial derivativ with respect to x of the function f(x, y)= 4xy + 2x…

A: To find out the correct option.

Q: Which is not the about f(x) = |x|? Continuow at O no targent line at 0 Derivative from left at O is…

A: Use the function value to evaluate which one is false

Q: √x +3 xy + 7 y). If f(x, y) = the domain of ƒ(x, Select one: True O False then the point (1, −7) is…

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Q: For the limit, lim (x,y)-(0,0) if we approach along x-axis, we will get 0. Select one: True sin(x² -…

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Q: Let Find fa, fay and fryz f(x, y) =In(xy)-26x¹0 y 10

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Q: k will the function f(x) = kx²-x²³ have a point of inflection at x=2? For what value of

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Q: z = e Select one: True False In (2-y), dz and x = s² - 6t, y = t - s, then the value of when t = 4…

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Q: Where is f(x)= x³ differentiable? (interval)

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Q: The limit exists and is equal to 0. Select one: O True O False lim (x,y) →(0,0) 36x²+25y² 6x+5y

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Q: If f(x, y) = x²y + cos(x) then (fx, fy) = (2xy + sinx, x²). Select one: O True O False

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Q: 6. If z = x + iy = (x, y), then the equation z²+z+ 1 = 0 is written as (x,y)(x, y) + (x, y) + (1,0)…

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Q: Evaluate √xdx f 1+x

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Q: Let u = (4,-1,-1) and v= (2,-2, 2x + 1) be two vectors in space. Find alle ER such that u and v are…

A: The given vectors are u=4,x-1,-1 and v=2,-2,2x+1