Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces x2 + y? = 4 and z = = 2x3. r(t) = (

Q: Find an equation of the tangent plane to the given surface z = x sin(x + y) at the point (-1, 1, 0).

A: Given,  z=x sin(x+y) ⇒x sin(x+y)-z=0 Let f(x,y,z)=x sin(x+y)-z Recall: The equation of the tangent…

Q: ZX = 24, XY = 10, and YZ = 26. Find cos Y. %3D

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Q: sin y dV, where E lies below the plane z = x and above the triangular region with vertices (0, 0,…

A: Given, the region E lies below the plane z = x and above the triangular region with vertices 0,0,0,…

Q: Find equation of the plane tangent to the following surface at the given point. an z = tan(xy):…

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Q: Identify and sketch the graph of the following SURFACES. x² + y² = sin²z, z = [0, π]

A: Any point on the 3D plane is represented using the ordered pair: x, y, z. A graphing utility can be…

Q: find the area of the surface S: x² + y² + 2² = 4 -A <tan -^ (*) FO 6 < COS Cos FJ VI (2) 4 DEX TI 3…

A: The given Surface is                    x2+y2+z2=4 ........1where π6≤tan-1yx≤π3 and π4≤cos-1z2≤3π4…

Q: The area of the surface generated by revolving the curve y = V9 - x,-2 s xS 2 about the x-axis is…

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Q: sin xdx 3 S cos° x

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Q: Find the points on the surface x² −yz = 5 that are closest to the origin.

A: Let the point P be (x,y,z). The distance between the point P and origin is given by the formula…

Q: 1. dy dx x + y x

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Q: f(x) = x³, with 0 < x < 1

A: We know, the surface area of the solid that is obtained by rotating the graph of y=f(x) about the…

Q: Use Y=sin) and reductiori of order to find the generale soletion to the homogeneous differenticl…

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Q: 2. For the surface z = In(y+ Vx² + y²). (a) Find an equation of the tangent plane at the point (3,…

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Q: 4. Find the equation of the tangent plane to the surface Z = = 5tan(x) – sin(3y) at the point (xoyo)…

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Q: Evaluate f (x + 2y)dx + (y – 2x)dy around the ellipse C defined by x = 4 cos 0, y = %3D | C 3 sin…

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Q: Solve the I.V.P using [x = zry]. y di dx + (y cos ( 1 ) - x) dy = 0, y (0) = 262

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Q: 1. Find by integration the area of the surface of revolution generated by revolving the loop about…

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Q: Find the area of the surface obtained by rotating the curve y = cos 2x, x is an element of  [ 0,…

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Q: Use a scalar line integral to find the length of the curve r(t) = (20 sin , 20 cos ,5), for 0 < t <…

A: Given

Q: A particle was following the trajectory r(t) = (e', sin (2t), t), but it starts flying tangentially…

A: SolutionGivenA particle was following the trajectory r(t)= (et,sin(2t),t) , but it starts flying…

Q: Determine the linearity and solve for the general solution to the given DE * dx ecos y – x cot y dy

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Q: Compute f cos(Tæ) dæ + 10xy dy, where y is a part of parabola y = 3x? from the point (0,0) to the…

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Q: x+ y dydx = Inß ху %3D Find B.

A: The objective is to find the value of beta.

Q: Determine the points on the surface y2 + z2 − x = 8 that are closest to the origin. Solve problem…

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Q: 3. z = (c

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Q: Find an equation for the tangent plane to the surface 4xy6 + sin(rx) Z = at the point (1, 1, 4)

A: We have to find the tangent plane  of z=4xy^6+sin(πx) at (1,1,4)  Find the partial derivative with…

Q: Find the equation of the surface of revolution of x = z2 about the x-axis.

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Q: c. Based on the orientation of your rectangle would we integrate with respect to x or y? С.

A: Follow the procedure given below.

Q: Use polar coordinates to evaluate the double integral 2 1 – a²- dy dx. (1+æ? + y²)²

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Q: Differentiate parametrically to find X 1 t-1 y=t³+2 dy dx in terms of t:

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Q: 2 5. x = 1+t2 2 y= t(1+t?)

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Q: Find an equation of the plane tangent to the following surface at the given point. z = tan'(xy);…

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Q: - Evaluate the integral 4-z²-y² 1 dz dy dx Jo 4-z²-y² x² + y² + 2² using spherical coordinates.

A: To evaluate ∫-22∫04-x2∫-4-x2-y24-x2-y2 1x2+y2+z2 dzdydx

Q: Find the area of the surface obtained by rotating the given curve about the x-a T x = 5 cos (0), y =…

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Q: The surface area of the solid of revolution generated by rotating x = (y² + 2)²,1 < y s 2 about the…

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Q: Evaluate II| 6x(x2 + y2) dv, where E is the solid in the first octant that lies beneath the…

A: Since the integral lies in first octant so 0≤θ≤π/2 and z≥0.  Converting into cylindrical coordinates…

Q: Find the points on the surface 2a2+ ly? + 522 = 1 at which the tangent plane is parallel to the…

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Q: dy in terms of t: Differentiate parametrically to find dx 1 y = +2 t+1

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Q: 3. (a) Find the equation of the plane tangent to the surface given by f(x, y) = 2xª+2y^+7xy at the…

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Q: Find Ja xydx + sin(x)ydy, where C is the boundary of the triangle with vertices (0,0), (0, 1) and…

A: Let I is the value of given Line Integral.

Q: Find parametric equations for the semicircle x2 + y2 = a2, y&gt; 0, using as parameter the slope t =…

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Q: Compute the surface area of the surface generated by revolving the astroid with the parametrization…

A: In this question, we find the surface of revolution by rotating the given parametric curve around…

Q: Find the point on the graph of z = (x² + y)? at which the tangent plane is parallel to the plane 2x…

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Q: On the surface z =, in what direction is z increasing most rapidly when x =1 and y = 2.

A: A function z=f(x,y) increases most rapidly, at a point (a,b) , in the direction of the gradient…

Q: f(x) = V4x +1, = V4x + 1, with 1< x < 5

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Q: Find a cubic approximation of r(θ) = (θ 2 , eθ , θ) at θ = 0.

A: given rθ=θ2,eθ,θ to find - cubic approximation at θ=0

Q: Find where) i ) et u*rany tany = 1 , U= xInx (use chatn reule ) ii) coscxy) - * + e+y) = 2 yz

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Q: The area of the surface obtained by rotating the curve y = et +e asxsb, about the x-axis is 1/2 e2 +…

A: Find the surface area rotating the curve about x axis