QI/ Find the tangent plane of the function f(x, y) = e**+y* at (0,0). Is it parallel to the plane 2x + 3y- z 1 or not? Why?

Q: The surface z=f(x,y) intersects the plane x-2 along the curve C which has equation of dy Find at the…

A: Given Data: The equation of the curve is: z=13y3-y2 The point at which derivative is required is: x,…

Q: Find the area in the first quadrant bounded by the curve Y = 4 – x^2 and the axes using horizontal…

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Q: How do you compute torsion?

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Q: The possible error involved in measuring each dimension of a rectangular box is ±0.1 millimeter. The…

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Q: = 21 which is parallel to the plane Find the equation of tangent plane to the surface x? + 2y? + 3z2…

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Q: Calculate directional derivatives and gradients in three dimensions. Find an equation for the…

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Q: Calculate integrate integrate sinx/x da Where R is the triangle in the xy plane bounded by the…

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Q: A disk of radius 4 cm has density 14 g/cm? at its center, density 0 at its edge, and its density is…

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Q: Describe the region R in the xy-plane that corresponds to the domain of the function. f(x, у) X- y…

A: Denominator should not be 0.

Q: derivative Shoue that the total in cylindrical coordlinates is givenr by DV Dt

A: To show, the total derivative in cylindrical coordinates is The total derivative in cylindrical…

Q: The tangent plane and the normal line of the surface y = x² + z – 6 at the point (2, -1, 1) have the…

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Q: 55. A point moves along the intersection of the elliptic parab- oloid z = x+ 3y and the plane y = 1.…

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Q: Find an equation of the tangent plane to the given surface at the specified point. z = square…

A: z=xy Partially differentiating with respect to x, we get zxx, y=y·12x=12yx Partially differentiating…

Q: Find an equation of the tangent plane to the surface at the given point. 6x² + 2y² + 4z² = 30, P=…

A: NOTE: Refresh your page if you can't see any equations. . the function f is

Q: Tangent to the parabola z = x² + 3y² , x = 1 , at point ( 1, 2, 13

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Region bounded by: y = x+1, y = -x + 4, x = 0 Rotate about: y-axis %3D

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Q: A flat plate (lamina) with uniform density p occupies the region R bounded by the curve y = x? + 1,…

A: follow next step

Q: What is a di¡erentiable curve’s unit tangent vector? Give an example.

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Q: Point W is the centroid of triangle TRV. VX = 204 and RW = 104. The length of RY = ____.

A: We have the given triangle as It is given that Point W is the centroid of triangle TRV. VX = 204 RW…

Q: What are the expressions for the gradient and Laplacian in cylindrical coordinates (z,r,φ)? Simplify…

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Q: Example: find the tangent plane and normal line of the surface f(x, y, z) = x +y² +z² = 3 at the…

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Q: Find the tangent plane to the equation z = 3x? – – 60) - y² – 4y at the point (4, 2, - -

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Q: dentify the length of the curve 9y2 = 4x² from x = 0 to x = 3. %3D

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Q: ди dt 00 dx2 ди u(0, г) — 0 %3DИо, %3D -h (u (1,1) — ио), һ>0, t>0 and u(x, 0) %3D f(x), 0<x<1. dx

A: We are given the following boundary value problem. k∂2u∂x2=∂u∂t,        0&lt;x&lt;1, t&gt;0u0,t=0,…

Q: Find the center of mass of a thin plate of constant density ô covering the region between the curve…

A: It is given that, y=5sec2x,  -π4≤x≤π4   Since the density is constant so we'll not require this to…

Q: A ring in the shape of the curve x + y = a² is formed of thin wire weighing |x|+ |y| grams per unit…

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Q: region in the xy-plane bounded by the curves y= Vx ,y=0 and x=1. (c) xy dV, where E is the solid…

A: We have to evaluate the triple integral ∭E xy dV over the region E, where E is the solid tetrahedron…

Q: Determine the surface area generated by revolving the curve y =x'over the interval 3 [0, 2], about…

A: Given that, Curve y=13x3 over the interval [0,2]   We have to Determine the Surface Area generated…

Q: Consider the family of curves y I 1+ GI

A: We have y=x1+c1x Differentiate with respect to x: dydx=ddxx1+c1x⇒dydx=1+c1xdxdx-xd1+c1xdx1+c1x2…

Q: How do Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem relate to the Fundamental…

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Q: plane to the area given by the implicit equation at point A=[7, −1, 7]. F(x,y,z) = exy+z…

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Q: Find the moment of inertia with respect to the y-axis for a flat plate covering the region bounded…

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Q: integra 18 uent to I V +1

A: We have to choose the correct answer from the given options according to the given information

Q: tangent plane and the normal line to the surface

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Q: A thin plate of constant density d = 1 occupies the region enclosed by the curve y = 36/(2x + 3) and…

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Q: Solid created from these conditiong limited to 0eyet fiest actant on ly Positive xy-plane

A: y=xx=y2,0≤y≤10≤x≤y2z=1-yy=1-z0≤y≤1-z,0≤z≤1V=∫01∫01-z∫0y2 dx dy dz

Q: Stokes' theorem is given by curlF = SP which is a generalization of Green's theorem. i) State TWO…

A: i) To state two dissimilarities between Green's and Stokes' theorem.

Q: Calculate the flow rate of a fluid with velocity field v = (4x, 2y, x²y) (in meters per second)…

A: Given, V=4x,2y,x2yand the surface is S: x32+y42=1 in the xy-plane.   Let us parametrize the surface…

Q: 9. Find equations of tangent plane and normal line of surface e -z+ xy 3at point(2,1,0). %3D

A: Given a surface fx,y,z=ez-z+xy=3. To determine the equation of the tangent plane of the surface at…

Q: A thin plate of constant density δ = 1occupies the region enclosed by the curve y = 36/(2x + 3)…

A: Given that : A thin plate of constant density δ = 1 occupies the region enclosed by the curve y =…

Q: find the center of mass of a thin plate of constantdensity d covering the given region. The region…

A: Consider the graph of the function given in the question: Here we have: The formulae that will…

Q: Region Ris enclosed by the curve y = 2 Vx – 3, the line y = 4, and the line a = 3. y = 2/z – 3 y = 4…

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Q: Q1,- A- Locate the centroid (X only) of the shaded area y=12-3x Fig.L.A

A: X= My/M  Y= Mx/M  X,Y are coordinate of centroid.

Q: Find an equation for the tangent plane to the surface z + 4 = ry* cos(z) at the point (4, 1, 0)

A: Solution: The objective is to find an equation for the tangent plane to the given surface

Q: Find the center of mass of a thin plate of constant density ô covering the given region. The region…

A: Given :-  The region bounded by the parabola x = 4y2 - 2y and the line x = 2y. To Determine :-  The…

Q: partial derivative F(x,y,z) = arc sin (xy/z)

A: Given that: F(x, y, z)=arc sin(xy/z)

Q: Find the length of arc of the curve y = √sec²t - 1 dt from the point where x = -to the point where x…

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Q: Find the center of mass of a thin plate of constant density & covering the region between the curve…

A: Answer

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.