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Q: The product rule can be applied to the divergence of scalar f times vector    G-› as: ∇-›·(fG-›) =…

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Q: Does the Divergence Theorem apply to surfaces that are not closed?

A: By Stokes' theorem:

Q: (c) If and are smooth scalar fields, show that V x (6V) = Vox V

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Q: Please don't provide handwritten solution .... ) Consider the space R^2 equipped with the sunflower…

A: The objective of the question is to identify the set of points in R^2 that forms a ball of radius 1…

Q: If u and v are two vectors in opposite directions, then : Select one: a. u equals a negative…

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Q: (d) Let f(x, y) = 2x² + xy-y². Prove that the directional derivative of f(x, y) at point x = (3,-2)…

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Q: A variable plane pes through a fixed point (a, b, c) and meets the uses at A, B and C. Show that the…

A: Given that a variable plane passes through a fixed point (a, b, c) and meets the uses at A, B, and…

Q: a) Sketch the graph of 7(t) =and show the direction of the increasing t, where 0 c) If 7(1)…

A: The vector field is rt=cost, t, sint. Now, if yt=t, then x=cosy and z=siny. Thus, the vector field…

Q: Show without using the Heine-Borel theorem that the line R is not a compact set in R ^ 2

A: The proof is done using the definition of compact set. A set S is said to be compact if and only if…

Q: Verify greens theorem form 1 for F=x^3i+yj and c is the circle x^2+y^2=1, oriented anti clockwise

A: Find ∫CFdr, the line integral of F, where C is the circle x2+y2=1, oriented anti clock wise…

Q: #12- Fnd the indefinite integral of the follaung funchon and check the result by differentionion.

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Q: Define p: R^2 x R^2 to [0, infinity) by the rule p(x1,y1),(x2,y2)=squareroot((x1-x2)^2+(y1-y2)^2)…

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Q: Q2) homeomorphism. Prove or disprove: The function f: (R, T1) - (R, 13) defined by f(x) = 3x is a…

A: Clearly the given function f(x)=3x is continuous. Now we want to check whether it is bijective,

Q: In each part, find a function that satisfies the requested conditions. (justify your answer). The…

A: According to the question, I).  The partials exist and the other directionals do not exist.This is…

Q: Divide "a" into three parts such that their product is maximum. (Explain with calculus method)

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Q: Shoe that Hhe p qiuen by norm on (on ho f be given by a scalar prodluct

A: We need to show that the norm on l∞ given by: x1,x2,…,xn,…∞=supxj: j=1,2,3,… can not be given by a…

Q: O Differniate the function after a di fferewt form first rewirming the functio^ * Dont use Product…

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

Q: xy² (0) (Use syntax like [3,-4,5] for vectors.) Let F (x, y, z) = xz5 What is the value of curl F at…

A: The vector F(x, y, z) is given. We have to find the value of curl F at (3, 2,1) .

Q: * Use the Grom Schmidt process for thi two_ dmensional space: 2 3. 4 2

A: Gram Schmidt process is given by: uk→=vk→−∑j=1k−1uj→⋅vk→|uj→|uj→   v1→=201, v2→=3-51, v3→=042,…

Q: Evaluate the curl: V x (yz³, x³z, ry³) =??? 3

A: In this question we will use basic of calculus i.e concept of vector calculus. First we will simply…

Q: 5. Quadrilateral MATH has coordinates M(-3,-1), A(6,2), T(5,5) and H(-4, 2). Prove that…

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Q: 3x²-by?-9x ニ Local maximum valuels) = ? Local minimum valuecs)= ? Suddle point(s) こ (xy.f) = ?

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Q: Find the domain of the vector functions, ?(?)�(�), listed below. using interval notation. ) ?(?)=⟨…

A: To find the domain of the vector function r(t)=⟨t−3,t2−4​1​,t1/3⟩, we need to consider the values of…

Q: If a line segment AM=a moves in the plane XOY remaining parallel to OX so that the left endpoint A…

A: Let the coordinates of A be (x,y) and that of M be (h,k).Since AM is parallel to OX,h=x+a and k=yor…

Q: Justify that (•, ·) defines an inner product on R?. the function (', ·) defined on R? as follows: U1…

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Q: Consider the infinite geometry R^2, where points are (x, y) ∈R and lines are ax + by + c = 0 with a,…

A: We have to show that R^2 is an Affine plane.

Q: (b) Every continuous map S? →T² is homotopic to the constant map.

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Q: o let fon= (x-1)? +2; xzl a find f-(x),domain range b) confirm fof cigraph t Uning yix using…

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Q: 2) Given f(x,y) Dand some domain, vertica) traces, horizontal traces then gruph the surface. 10…

A: Given Data: Let us consider the given function is, fx,y=101+x2+y2. To Find: Domain, vertical…

Q: defermine whether is or divergent tonvergert Inin)

A: The above series is split into two as sum of two series as follows…

Q: 04/ Bind the differential of Hthe Punction at the indicated number f(x)- JzxAY x =4

A: We can find the differential at the indicated point as below

Q: find for me all points where G is preserving orientation?

A: Sol:-To determine where G is preserving orientation, we need to calculate the Jacobian matrix of G…

Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that has a power series…

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Q: Find the dircetiond Derevitive ef the Fouctiom 19(x2y)= Xye? at pl68, in the direchen oF Ol0,Og0)…

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Q: Let T : R^2 → R^3 be a linear map. What are the possibilities for the pair of numbers (dim Null…

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Q: 9 find the cqu. f Plane that Contains the two line Ś: X-1=3+ 6=そ X=リニで-4 and Passes through origin?…

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Q: (a) Give examples of three distinct vectors vị, v2, vz in the vector space R³ such that vz E…

A: Let v1 = {1,1,1}v2 = {2,3,4}v3 = {1,2,3} Here  v2 = {2,3,4} = {1,1,1}+{1,2,3} = v1+v3

Q: What is the translation from quadrilateral EFGH to quadrilateral E F'GH'? E -6 15 14 -3 -2 -1 4 F G'…

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Q: tix)=Dx²-6xs hurizontal tumpant eme fir). f')=D(x2-6xj Find x-value

A: Answer is The value of x is 0,3,6 And in the given question your differentiation is wrong. Because…