Instructions :- Write answer on the paper and upload PDF file in the Moodle. Do not write any answer in the box. Problem - 24: Given f(x, y) = e Y – x'y', show that fæy = fyæ.

Q: Question 9 To evaluate J y-cse(y?)cor²(y³)dy, we let u =cse(y³) A) True B) False

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Q: Match the equation r(t) = cos( t)i + sin( t)j + t2k, −1 ≤ t ≤ 1 with its graph.

A: Given Data The equation is r(t)=cos(t)i+sin(t)j+t²k .   Let,

Q: The equation dx ¡y = xy can be classified as FOLDE and Bernoulli's equation.

A: Given that Diffrancial equation dydx+4x2y=xyTo identify the diffrancial euqation bernoullis equation…

Q: The position of a particle in the xy-plane at time t is r(t) = (t+2) i+ (t- + 3) j Find an equation…

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Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: S¤(t) = ly(t) = 3t2…

A: We can make it easier for you.

Q: Question 2 Express the curve by an equation in x and y given x(t) = 11 – sin(t) and y(t) = cos(t).…

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Q: 5) Sketch the curve X = e', Y = e?t + 1

A: Given, The curve  X = et  and  Y = e2t+1 We have to sketch the curve.

Q: Determine the roots of the indicial relationship for the Frobenius method applied to the following…

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Q: Question 7 (a) Find if x² + y² +xy=1 dy dx (b) Identify the nature of the stationary points of y =…

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Q: The equation + dx y = xy can be classified as FOLDE and Bernoulli’s equation. A True False

A: True.

Q: t or points for each ase portrait on this page. dx = 2x – 2y – 4 and- = x+ 4y +3 dt dt GURE 6.1.

A: Given

Q: Question 15 Let w = x'+ V9x, y= w°. Find ay dx

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Q: If – 3x + xy – 4 = 0 then find dy da? at the point (-2, 1) in simplest form.

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Q: Consider the following Bernoulli equation. Use a suitable substitution to transform the equation…

A: Consider the following Bernoulli equation. Use a suitable substitution to transform the equation…

Q: Question 7 dy Find dr where y is defined implicitly by the equation a4- 5a y7 8 |3D dr 5y7 10y 422…

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Q: Find dy/dx and (d^2)y/dx^2, and find the slope and concavity (if possible) at the given value of the…

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Q: Find T, Ñ and B for the curve 7 (t) = (5 cos(4t), 5 sin(4t), 2t) at the point t = 0 Give your…

A: the given curve is  r→(t)=5cos(4t),5sin(4t),2twe have to find a) T→(t)=unit tangent vector at t=0b)…

Q: x =t – 1, y = t2. B. Sketch the graph of the curve r = 3 cos 0.

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Q: Question 19 Express the following parametrized curve by an algebraic equation in terms of x and y: x…

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Q: baunded by y= e y=1, X=2a ŷ rotate about =a

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Q: 6. Find the angle above the horizon of the airplane as seen by the observer. Problem 5. Two traffic…

A: Given:

Q: The motion of a particle is defined by the following equations:     dx/dt = x-2y and dy/dt = 5x-y…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Question 4 – Find the end points and control points of the following Bezier curve with t e [0, 1]:…

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Q: Question 15 Using the change of coordinate system, the integral (z² + y²) dydæ would then take the…

A: Here we have to change the coordinate system.

Q: Dind da 2 uit

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Q: dz dz and ду Suppose z is a function of r and y, and tan Vy? + x2 = z"e6y. Solve for

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Q: Question 24 2ay" =17 when t=V2. y' If x= Arctant3, y=/1+16, find the value of a if A 2/2 - 2/2 В ©…

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Q: Pपा+ with a focus at co,-1) 'and directrix y=l

A: Vertex will be the midpoint of y=1 and (0,-1)  That is (0,0) So, (h,k)=(0,0)

Q: Q4. Given the data points 3 ソーf(x) 7 11 28 Use Lagrange's Method to determine y at x-1, also find x…

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Q: If y = e then y – y' + e*y is equal to %3D eet

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find at the given point without eliminating the parameter. dx2 1?, y = , X = 2 t = 2 3

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Q: Eliminate the parameter t to find a Cartesian equation in the form x f(y) for: S¤(t) ly(t) 3t? 4 +…

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Q: Find the equation of the set of antiderivatives at any point (x, y) whose slope is ei sin"(1- x?)2.…

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Q: Question 7 (a) Find if x² + y² + xy = 1 dy dx (b) Identify the nature of the stationary points of…

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Q: Question 2 Express the curve by an equation in z and y given z(t) = cos(t) and y(t) = 3 sin(t). a)…

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Q: 9) i) The equations of two circles S, and Sz are given by S:x+y +2x+2y+1=0, Sr +y-4x +2y+1=0. Show…

A: In the given question we have to solve the first part of the question 9. in this question we have to…

Q: Question 8 Find the coordinates of the point(s) on the curve y = Va + 4 that are closest to the…

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Q: If the length of a curve from (0,–3) to (3,3) is given by [ V1+(x² – 1)² dx , which of the following…

A: Length of a curve formula.

Q: Show that E(Y) = 0

A: The E(Y) can be calculated as E(Y)= ∫-∞∞y·fydy

Q: Question 19 Express the following parametrized curve by an algebraic equation in terms of x and y: x…

A: We have to find

Q: Question 3 Consider the function f(r, y) = 2x + 4y² %3D and the curve y(t) = (sin t, cos t), te…

A: Introduction: For a given function fx,y and a curve rt=xt,yt, their composition is frt=fxt,yt. The…

Q: Find the solution of the equation dy -y = x dx | subject to the condition y(1) = 2. %3D

A: Given differential equation is xdydx-y=x and y(1)=2

Q: dz dz and Suppose z is a function of æ and y, and tan Vy² + x² = z#e6y. Solve for

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Q: dy +y = 12 e?Xy dx %3D12€

A: Bernoulli's equation: A differential equation of the form dydx+Pxy=Qxyn for all natural numbers n.…

Q: 9) xdy- ydx = (x² + y ² ) ex dx a) artan. * =* b) arctan X = ţ c) auctan $ d) none of the above etc…

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: Find dy/dx and d'y/dx, and find the slope and concavity (if possible) at the given value of the…

A: slope is defined at dy/dxand concavity is defined at d2ydx2

Q: +1 x² Find I = dx use two and three points of Gaussian-Quadrature

A: