Find domain and range of the funetion f(x, y) In[e-x' -y'1

Q: Consider the functions z = -8 ex In y, x= In (u cos v), and y =u sin v. dz as a function of u and v…

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Q: = x2 - 4x + 1 with domain [0, 3] f has ---Select--- v at (x, y) = f has ---Select--- v at (x, y) = f…

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Q: Find the perticular number or orthogonal trajectories of x2+cy2=1 passing through the point (2,1)

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Q: find taylor degree of polynominal at degree of 4 at c is pi/4 for f(x): sin(x)

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Use the Existence and Uniquness Theorem to verify, with initial value (-2,-1): y' = xy2

A: Consider the differential equation y'=xy2 with initial condition -2,-1 Compare the differential…

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: Differentiate ysin(1/y)=1-xy

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Q: 5. Deduce the standard linear approximation of 1 x2+y2+z2 at Po(1,2,3).

A: The general formula of the standard linear approximation for f(x,y,z) is generally given by,…

Q: Expand x'y + 3y - 4 about the point (1, -2) by Taylor' s theorem.

A: Let, the given function be fx,y=x2y+3y-4 and the given point is 1,-2

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: Given, f(x)=1x, a=0.9 now find linearization f(0.9)=10.9=109 so linearization at 910,109…

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: 2. Let f(x, y,2) = z-sin(xy), x = t, y = In t, z = e. Find derivative of f directly and by using…

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Q: Determine two functions, defined on the interval (−∞,∞)(−∞,∞), whose Wronskian is given by…

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Q: (6) Find the orthogonal trajectories of the 3C cos 0, where C family of curves r being parameter.

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Q: For z = arctan(x² + y²): Compute all first and second order partial derivatives. Find the…

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Q: Determine the orthogonal trajectories of the family of electric field lines described by the family…

A: Given    x-c3+y2-c23x-c=x3   differentiate  w.r.t.x    3x-c2+2ydydx-3c2=3x2⇒2ydydx=3x2-3x-c2+3c2…

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: Obtain the orthogonal trajectories of xy = C and compute for the positive value of y at the point…

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Q: A stretched string of length 20 cm is set oscillating by displacing it midpoint from the rest…

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Q: Compute the partial derivative fxxyz for f(x, y, z) = cos(cos(x3 + z2 )) + x2 ln(y2 + z2 ).

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Q: Use chain rule to find given x² + 2y² + z² and x os (st), y %3D Cos

A: Solve the following

Q: Find both first partial derivatives. z = cos(10xy) az ax az ||

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Q: If X; derive the moment-generating function (mgf) of X?. Ν (μ, σ) :

A: Given X~ N(mu, sigma^2) We want to find the mgf of X^2

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: The nearest integer to a=-0.9 is -1 because at this point, we can easily find the function's value…

Q: Let f(x, y, z) = 4xy – z², x = 6r cos(0), y = cos (0), z = 3r. Use the Chain Rule to calculate the…

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Q: 4. Find the orthogonal trajectories of the family of curves: y = ke* %3D

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Q: (a) find the local linearization of f(x)=fourth root(x) at x=16 (b) Use the linearization to…

A: It is a linear approximation problem

Q: The

A: Below is sketch of  the given function.    Rotation about x axis will give a volume in 3D plane.

Q: Solve MXVN at (1,1-1) When M = (2yz)i – (x²y)j + (xz²)k and N = 2x²yz³ Show the graph after it.

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Q: Use forward, backward and centered difference approximations to estimate the first derivate of: tx)…

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Q: Find the orthogonal trajectories to the family of curves: r=c- (in y -1).

A: Orthogonal trajectories can be find in the following way: (i) differentiate given family of curves,…

Q: plot Y funetion of as over Hhe Peenge ☺.0l <*< l00.

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Q: Compute the partial derivative of h(x, z) = e4xz-3x²z. (Use symbolic notation and fractions where…

A: In this problem first we need to partially differentiate the function with respect to z and then put…

Q: Find the first partial derivative of w = In(1 + )at (2,0, – 1).

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Q: Find both first partial derivatives. Z = In

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Q: 5. Find the orthogonal trajectories for a family of circles tangent to the at y-axis.

A: Here we have to find the orthogonal trajectories for a family of a circle tangent to the x-axis and…

Q: Find and classify all the critical points of f(x, y) = x³ - y³ - 8xy.

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Q: Find the first partial derivatives of the funct f(x, y) = x8 + 7xy5 fx(x, y) =

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Q: find all the second partial derivatives of Z and show complete solutions Z= tan-1 ( x2 / y3 )

A: Partial derivative of the function Z=f(x,y) is denoted as The first partial derivative∂Z∂x, ∂Z∂y The…

Q: 3z2+x 30. If z – xz – y = 0, prove that- =- ax dy (3z²–x)³*

A: Let's find.

Q: 5. Find the orthogonal trajectories for a family of circles tangent to the y - axis and centers at x…

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Q: Find all the second order partial derivatives of the function : f(x, y) = In 4ry + sin 3ry + e4z-3y

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Q: Explain how successive over relation is obtained from the Gauss-Seidel method.

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Q: I Sdve for dydx using the four-step rule 2. Y = x- x 2.

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Q: Find the orthogonal trajectories of the functen X + ce-X which is . passing Thieugh (-2.0)

A: We need to find the orthogonal trajectories of the function y=x+ce-x, which is passing through (-2,…

Q: 5.If the tangent 1ine to the functlen fx)= axt-6x at X=- has the equatfon. y= 3x+2then 6=?

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