QUESTION 17 Let a , b and c be the last three digits of your student ID and let d=max(a,b,c). 2 How many points are there on the surface z = dx +y such that the tangent plane to the surface is parallel to the plane dx +y+z =0 1 O O

Q: QUESTION 5 What is the best description of the surface parametrized as x=3+u, y=3-v, z=3+u+2v. with…

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Q: QUESTION 4 What is the best description of the surface parametrized as x= 3sinucosv, y=3sinusinv,…

A: The parametric equations for the sphere of radius r unit is x = r sinucosv , y = r sinusinv ,   z =…

Q: Question 1. Use Stokes' theorem to evaluate SF · dr, where C is the circle x2 + z² = 2, y = 1, and F…

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Q: Problem 3. Calculate the first fundamental forms of the following surfaces: (a) x(u, v) = (u - v, u…

A: According to guidelines we should have been able to solve only first question at a time #3

Q: Question 1: Let L denote the intersection line between the planes 2x-y-3z=4 and 2x+y-z=2 A)…

A: Given that L is the line of intersection of the planes 2x-y-3z=4 and 2x+y-z=2

Q: QUESTION 7 Let P be the tangent plane to the surface z=x2+2y2 at the point Q=(-1,-1,3). Which of the…

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Q: Question 2. Use Green's Theorem to evaluate f, 2y?dx + 5xydy, where C is the boundary of the…

A: We have to evaluate the integral ∫C2y2dx+5xydy where C is the region between the circles x2+y2=1 and…

Q: Question 13 Solve the problem. Find parametric equations for the normal line to the surface x² +…

A: Find parametric equations for the normal line to the surface x2 + 2xyz + y2 = 4z2 at the point (1,…

Q: 2) The (Beltrami) pseudosphere is given by the chart x Cu,v) =( Coscul Sin(v), Sincul Sin(vl,…

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Q: (b) A = 2pza, + 3z sin ø a, – 4p cos p a̟ and S is the surface of the wedge 0 0 < ¢ < 45°, 0 <z < 5

A: Let us solve the b part step by step with given A value

Q: Let a , b and c be the last three digits of your student ID and let d=max(a,b,c). How many points…

A:

Q: Question 22 Question 4 (6 + 1+7+ 6 = 20 marks). Question 4 b) ii) - 6 marks Evaluate the line…

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Q: Problem #8: Use Stokes' Theorem to evaluate F. dr where F = (x + 9:)i + (7x + y) j + (6y – =) k and…

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Q: Question # 4: Let and y = For what value(s) of h, is y in the plane generated by vi and va?

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Q: a) Consider the surface z = Find the tangent plane to the 3. surface at the point (4, 3, 5). (4.04)3…

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Q: 3. Use Stokes theorem to evaluate fa. In each case C is oriented counterclockwise when viewed from…

A: As per our company guidelines, We are supposed to answer only one question and rest can be reposted

Q: Let a , b and c be the last three digits of your student ID and let d=max(a,b,c). How many points…

A: Let a,b and c be the last three digits of your statement ID and let d=max(a,b,c) Here we have to…

Q: Problem 8: Given a general closed surface S for which the position vector r = 1,e; and normal n are…

A: Given a closed surface S and its position vector r→=xiei and the normal is n→. To derive the formula…

Q: 3.use Greens theorem S(1+x dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0).(1,3) oriented…

A: "Since, you have asked multiple questions, we'll solve the first question for you. If you want any…

Q: Question 5 Find the surface area of that portion of the surface z = V4 -x that lies above the…

A: Option (B) is correct

Q: Question 8. Consider the surface defined by x² – - = 1. Draw the traces of this surface…

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Q: Problem 2: Verify that the two sides of Stokes are equal for F = of the plane 5x + 2y + z = 1 in the…

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Q: a. Which of the following surface graphs represents f(x,y) = y²? OA.

A: Given, the surface                           z=f(x, y)=y2

Q: Find the equation of the tangent plane to *+ y? at the point (2, –3, 10) the surface z = 4 O x + 4y…

A: We have to find

Q: QUESTION 7 Let P be the tangent plane to the surface z=x2+2y2 at the point Q=(-1,-1,3). Which of the…

A: Given that  Z=x^2+2y^2  Point (-1,-1,3) To find teh point lies in p

Q: s) The given curve is rotated about the x-axis. Find the are √2x +3,0 ≤ x ≤ 6. of the resulting…

A: Introduction: The formula for the surface of revolution of the curve is given by,…

Q: The equation of the tangent plane to the surface yey +z =0 at the point (0,-1,1) is az+by+cz = 1.…

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Q: Problem 6. Use Stokes' Theorem to evaluate [ ſs(-y,x, ryz)dS where S is the part of the surface 2 +…

A: From the given information. The Surface equation is . The vector function is . From Stokes Theorem,…

Q: Question 4 Let w aXu(q) + bX.(@) € T,S such that |lw||= 1. Then the normal curvature to the surface…

A: Solution and explanation is below

Q: Question 7 2 pts Find the curvature k of the x2 curve C : :1 at 9 | 16 + the point (4, 0) 9. 3 3 16…

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Q: Question 8: The curve C in the ry-plane is parameterized by r (t). Find a parameterization of the…

A: Given:r→'t=4, 4e2t, 2costr→0=0,1,0

Q: Question 2. Consider the parametrized surface S: F(u, v) = (u sec v, u tan v, u?) (-o < u < 00, -1/2…

A: The general form of the parametric equation of the curve in three dimensional space is given by…

Q: Question 18 Find the surface area of that portion of the surface 2 = V4 -x that lies above the…

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Q: Question 2 Suppose an object is moving along the unit circle. (æ(t), y(t)) Find the correct relation…

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Q: Question 2 Let F(x, v. 2) = -2y7 + 2xj. Use Stokes' Theorem to find 17-d7, where C is a circle…

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Q: QUESTION 3 Which of the following is an equation for the tangent plane to the surface z= xy at the…

A: Tangent palane ti the surface

Q: The tangent plane to the graph of the surface z=In(x2+y?) at the point (1,0,0) contains point…

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Q: QUESTION 7 The tangent plane to the graph of the surface z=In(x2+y2) at the point (1,0,0) contains…

A: To find the value of t

Q: The tangent plane to the graph of the surface z-In(x<+y) at the point (1,0,0) contains point (3,3,t)…

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Q: B. Let C be the curve y = 1 – x2, 0< x < 1. If C is rotated about the y axis find the area of the…

A: our objective is to calculate the surface area.

Q: Ex.5 Given the Jordan curve y that is the counterclockwise oriented boundary of the set T= {z=x+iy :…

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Q: 33. Figure 14.13 shows the saddle-shaped surface z = S(x, y). (a) What is the sign of f,(0, 5)? (b)…

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Q: Question 2 Let D1 be the solid in space that lies in the first octant x, y, z > 0, and be- tween the…

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Q: Question 2 Consider the function f (x, y, z) = x² + y' – xyz Find the equation of the plane tangent…

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Q: Which of the following is the equation of the tangent plane to the surface z=x2 - x+3y² +y at the…

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Q: (b) A = 2rza, + 3z sin ø a, – 4 rcos o a̟ and S is the surface of the wedge 0 <r< 2, 0 < 0 < 45°, 0…

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Q: Problem II We consider a parametrization of a regular surface S, given by X (u, v) = (u+2v, 2uv, 2u…

A: Here the equation of the tangent plane to the surface will be Xu×Xv.x-6,y-8,z-2=0 where X=Xu,v is…

Q: Question 13 Find the center of curvature of the curve y=Inx at (1, 0). A (4, 3) B) (3, 4) (3, -2)…

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Q: Question 12 Find the center of curvature of the curve y=; e ¯*) at (0, 1). A) (0, 2) B) (1, 1) c)…

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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.