Suppose a Bézier curve is translated to x (t) + b. That is, for 0

Q: 2. If T = u? + v²,u = x+ y+z,v= ryz. Using the chain rule to find and when r = 1, y = 2, z = 3. Draw…

A: Given that: T=u2+v2u=x+y+zv=xyzx=1, y=2, z=3

Q: 7. Find a single initial vahue problem that admits the family of solutions y = e and then find an…

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Q: 7-The tangent of the curve x^2+y^2- 2xy3D0 at the point (1,1), is * O a. y=2-x. O b. y=x-2. C.…

A: We find equation of tangent to the curve

Q: 3. Determine the coefficients a, b, c, d that will make the curve y = ax³ + bx? + cx +d have…

A: We will find the value of a, b, c, and d as following .

Q: 2. Determine the coefficients a, b, c, and d so that the curve will satisfy the stipulated…

A: y=ax3+bx2+cx+d-1Critical points 1,0-2,27We know that at critical point dydx=0 or does not exist…

Q: 2. Compute F-dr where E= (x+ y,x-2z,z- y) and curve C is the line segment from (-3,5,1) C to…

A: Using line segment as the base of a rectangle, we choose the height to be the height of the surface…

Q: (1.-13) Show that the line integral (2xy+3)dx +(x² - 4z) dy-4 ydz is independent of path and (0.0,0)…

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Q: 4. Find the points on x² + y² + z² = 25, %3D where the temperature T(x, y, z) = x² + 4y² + 9z², is…

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Q: the Following is divergent

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Q: The curved surface of a rod of length L is perfectly insulated against the flow of heat. The rod…

A: .

Q: (6) Find the orthogonal trajectories of the family of curves r 4C cos 0, where C being %3D…

A: We have to solve given problem:

Q: 6. Let u (r, t) be the solution of the initial-boundary value problem ut = 9uzz 0 0, %3D uz (0, t)…

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Q: -2+z) ds over t e point (0, 0, 0)

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Q: Determine the coefficients a, b, c, and d so that the curve will satisfy the stipulated condition.…

A: Given curve is y=ax3+bx2+cx+d        (1) and critical points are (1, 0) and (-2, 27) We have to find…

Q: Find the approximate solution of the Poisson equation uxx + Uvy = -1, x| < 1, ly| < 1 u = 0 at x =…

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Q: 2Use divectional devivative delinihion of f(Hiy)=x y'at the divecionof ū =i jatthe Point (le2>

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Q: 10. Find the linearization, L(x,y,z) of the function f (x, y, z) = e* + cos(y + z) at Po (0,",").

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Q: (6) Find the orthogonal trajectories of the family of curves r= 2C cos 0, where C being parameter.

A: Consider the given curve. r=2Ccosθ          (1) Find the derivative of the given equation.…

Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy- 4y. Then: (1,1) is a critical point and f has a…

A: The given function is f(x,y)=6y2+4x2-12xy-4y

Q: A homogeneous string is stretched and its ends are at x = 0 and x 1. Motion is started by displacing…

A: The boundary conditions are y(0,t) = y(l,t) = 0 and initial conditions are y(x,0) = μ0sinπxl and…

Q: The first provider can provide at most 5 tons, and the second one at most 3 tons. Finally, in order…

A: (2): Given equation is x≥2y-1 Draw the diagram of domain P

Q: 7. Use the Method of Lagrange Multiplier to find the critical points of the function f(x, y, z) =…

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Q: will have a critical number -1 and a x Find a and b so that the curve y = ax³ + corresponding…

A: Given :f(x) = y=ax3+bx

Q: ナエ 人て、メ-(hrX)3 - kメんートで %3D Find critical puld (9 relative max relativi Saddle tレ10 or Cannot…

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Q: What are the control points of the splines Bezier curve from the two equations given below: a(x) =…

A: Given, ax=1+5x2+2x3...1bx=1-x+x3...2 The control points are lie on both the curves. So, to get…

Q: Consider the following information fz(x, y) = 2x³ - 2xy and fy(x, y) = 6 - x² - y². Use the Second…

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Q: 49.) Find the minimum distance from the point (2, 1, 4) to x + y + z = 4 by using the LaGrange…

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Q: (1. 1. 1) Evaluate the integral (5xy + 22°) dx + 5xf dy + (12z + 1) dz. (0.0.0) (Hint. Try the path…

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Q: The marginal moment generating function can be obtained from the joint moment generating function as…

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Q: A f lexi ble Stre tched string is constrained to move with Zero slope at one end x=0 whi le the…

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Q: 2 35) Find a curve through the point (-4, 1) whose length integral, 1 s y s 2, is L = 1 +

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Q: An object is moving along a path defined by the graph   x2+y2=2   Compute dy/dy, if dx/dt=2,x=−1,…

A: Differentiation application

Q: 4. Find the local maximum. minimum and saddle points of f(r,y) =1-2y+ In Vr2+y2 +3 arctan . %3D

A: Given: fx,y=x-2y+lnx2+y2+3 arctanyx

Q: (b) Show that the roots of y'(x) = 0 are x = 0, x = L, and x = L/2, so it follows (why?) that the…

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Q: 1 Verify Eular's theorem for z=- =(x²+xy+y*)' x²+xy+y² 2

A: The expression z=1x2+xy+y2=x2+xy+y2-1. We have to verify the Euler's Theorem.

Q: 1.6 Evaluate the line integral f x*dx + xydx where C is the triangle with vertices at (0, 0), (0,…

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Q: Let w = x°e4y cos(9z). Find the value of dwldt at the point (3, ln 5, 0) on the curve x = 3 cos(t),…

A: Given: w=x6e4ycos(9z)x=3 cos(t)y=ln(t+5)z=6tDifferentiating we…

Q: (4) Find the orthogonal trajectories of the family of curves z +y = 20C?, where C being %3D a…

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Q: 2. Sketch the grsph of au cxponcutial fuetion that satislics all of the conditions. Iorain (x E R)…

A: a) Given that domain is all real number. That means x takes all real values.  Range is y&lt;0, so y…

Q: Let us consider the hyperbolic PDE is utt with the initial conditions c2U, 0 0 %3D u(x, 0) = P1(x)…

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Q: ) Fnl the Vdume of the Selid enclesed by the curres "about the x-axS. y=e^, y=0 x =©,'x=/

A: To find out the volume of solid of revolution.

Q: Solve the DEQ given the initial condition (4,-2). Graph it on the slope field. 10 9 1 8- Let…

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Q: 5. Determine the coefficients a, b, c, and d so that the curve will satisfy the stipulated…

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Q: (6) Find the orthogonal trajectories of the family of curves r= 5C cos 8, where C being parameter.

A: we have to find the orthogonal trajectory for the given function

Q: 1. Find the orthogonal trajectories of the family of curve z + 3y = cy,where cis an arbitrary…

A: We will first find the differential equation of the of the given family of curves

Q: 1. Find the orthogonal trajectories of the family of curves y³ = 3(x – c). Draw a few representative…

A: The orthogonal trajectories are the curves that are perpendicular to the family everywhere.

Q: f(x, y) = 3x – x - 2y² + y* has I local max at (-1, –1) II local min at (-1, 1) III saddle point at…

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Q: Consider a Lorenz curve given by f(x)=x^n for 0≤x≤1 and n≥1. What happens to the Gini index G.I as…

A: Consider the given function. fx=xn The Gini index is defined as, GI=2∫abx-fxdx

Q: 1 Find skewness and kurtosis for the RV X with PDF f(x) = 2T -∞ < x < x.

A: PDF of X,  fX(x) = 12πe-x22, -∞&lt;x&lt;∞ So, μ = E(X) = ∫-∞∞x f(x) dx=∫-∞∞x 12πe-x22 dx=0 [as…