In Problems 1 2, evaluate (G(x.y,z)c, fG(x,y,z)dy and [G(x,y,z)ds on the indicated curve c. 1. G(x, y,z)= 2x+y-z, x = cost, y =sin t,z = 1,0s ts“. 2

Q: скоеалете 11 Tuesday # How many tangent lines to the curve y=x_q x-9 1 pass through the point (1,…

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Q: Problem IX: Evaluate |-ds where C is the portion of the curve y= Vx from the point (1, 1) to the…

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Q: MAT 100/B1 / Online Assignment / Online Assignment Find y in terms of x. dy 1 + 2, curve passes…

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Q: The cartesian equation of the curve x = vt ,y= 1– t is : (a)y = 1 – x², x 2 0 (b)y = 1 – x ,x 2 0…

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Q: 7. Compute T₁, T, and N(u, v) for the parameterized curve G(u, v) = (u² — v², u + v, u − v) at the…

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Q: 14. Calculate h(r) dr where h(x, y) = (6xy — y³)i + (4y+3x² − 3xy³)j and C' is the curve consisting…

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Q: 9. A point moves along a curve with a(t)= (2,6t, 12t2). Find its position function 7(t) if 7(0) =…

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Q: 1 Find the exact length of the curve: r(t) = , 6.

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Q: cerve X= Si▪ (Zt), y=Gs(±t), them dvaw the Culve

A: Given is the curve x=sint2, y=cost2 We need to eliminate t to find cartesian equation.

Q: 1z 2x² + y%, (1) z = 2 y;

A: Solution:-

Q: 5.PT. PLN has $140000 to invest. The alternative investments and the corresponding annual returns…

A: According tot he given information it is required to form an linear programming problem for the…

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Q: L et f(x)= x- 3x and P= (1, f (1)). Find (a) the slope of the curve y = f(x) at P, (b) an equation…

A: The given function is fx=x2-3x and the point is P=1, f1. Evaluate f(1) as follows. f1=12-31=1-3=-2…

Q: 2. The tangent line to the graph of y= e3-x at the point (3, 1) intersects the x-axis at the point P…

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Q: The cartesian equation of the curve x= vt ,y =1-t is : (a)y = 1– x², x 2 0 (b)y =1-x ,x20 (c) x = 1…

A: Eliminate t in given equation.

Q: 8) Wihat is the length of the pot Df the curve y2=(x-1)between the points (4,0) ond (2,4) ?

A: Let f(x) be a smooth function over the interval [a,b]. Then the arc length of the portion of the…

Q: 5. (This problem represents a very particular case of an interesting area of mathematical ap-…

A: To demonstrate that the shortest (differentiable) path connecting two points is a straight line…

Q: 1. Let y be the part of the curve y =r² running from (-1,1) to (2,4). Calculate ry dr + (x+ y) dy.

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Q: Evaluate (b) along the curve x = 21-2, y = 1+1-1². (3xy + y²) dz (a) along the straight line joining…

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Q: The region bounded by f(x) 2x² + 12x + 14, x = = 0 is rotated about the y-axis. Find the volume of…

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Q: In the xy-plane, the line tangent to the graph of 2 x² + xy + y² = 3 at the point (1, 1) has a slope…

A: Given equation is  x2+xy+y2=3  we need to find slope of the graph at (1,1)

Q: 13. Find the point on the curve 7(t) = (2 sin t, 2 cos t, t), 0<ts 7, where the tangent line is…

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Q: 1. Sketch the curve 4(x − 1)² — 9(y + 1)² = 36 in R². What is this curve? -

A: According to question,Given equation of curve,4x-12 + 9y+12 = 36

Q: Use de Moivre’s theorem with n = 4 to prove that cos(4θ) = 8 cos^4 (θ) − 8 cos^2 (θ) + 1

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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.