Q7:- Find the limit of the following vector functions:- (1) Lim (t²i+ 2tj) (2) Lim(+1i, (3) Lim (ti – 3j+t²k) t- 2 i+-j) 2. t 3t +2

Q: Q1. What is the divergence of the following vector function? v= yxx+ yŷ – yz î

A: Divergence of  vector function v is      div v =  ∇ v

Q: Q2. If F = (x² - y² + 2xz)ī− (2xz − xy + yz)j + (z² + x²), find the divergence of curl F and curl of…

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Q: Find a vector-valued function whose graph is the indicated surface.

A: To find :               Find the vector valued function whose graph is the indicated surface.

Q: 4. Find the divergence and curl of the following vector function: F(x,y, z) = ( arctan(ry),…

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Q: Evaluate a 3d divergence of 1/r^2 in the radial direction

A: V→=fr=r^r2∇·V→=1r2∂∂rr2·1r2         =0But above result is wrong. Because when we see flux in…

Q: : Find the divergence of the vector field At the point (2,4,1). F(x, y, z) = x² √yi+j+zk

A: We have to find the divergence of the vector field F(x, y, z)=x2y i^ +yxj^+zk^ at the point (2, 4,…

Q: Find the curl, the divergence and the potential (if it exists) of F = (2x + y², 2ry + 3y²z*, 4y°z³)

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Q: Find the divergence of the vector field F(x, y,z) = x²zi – 2xzj + yzk and the point (2, -1, 3).

A: Divergence of a vector field: The divergence of a vector field F = (P, Q, R) is given by, The given…

Q: Find the curl of the vector field at the given point. F(x, y, z) = x2zi – 2xzj + yzk; (9, -9, 5)

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Q: Express the following as a vector valued function 7 (t). 1. The line L defined by y+3=3x and z+1 =0…

A: We will express the line L defined by y+3=3x and z+1=0 hyperbola -x2-2x+2y2+4y=-2 as a vector valued…

Q: | Use Gauss Divergence theorem to calculate (5zi+ 4yj - 2: k).n dA over the sphere +y+ 9.

A: Here, let F=5x,4y,-2z⇒div F=∂(5x)∂x+∂(4y)∂y+∂(-2z)∂z=5+4-2=7

Q: 2. Use the limit definition to find the directional derivative of the given function f at the given…

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Q: The divergence of the vector G=i+siny j + 3k is :- -8y x3 + siny -8y x3 + cosy Option 1 Option 3…

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Q: Find the divergence of the vector field F→(x,y,z)=xyzi→−yzj→+xzk→at the point (8,3,2) .   Enter…

A: The given vector field is : Fx,y,z=xyzi-yzj+xzk To find the divergence at 8,3,2

Q: Consider the vector-valued function [f(x, y) xt – xy² [g(x, y) 2 Vx + y³x² [f(x, y) Which of the…

A: Find the Jacobian of the given matrix

Q: Consider the vector-valued function (t - 2)² In(t – 2), sin(t – 2) 12 - 4 12-3t+2 12 +t-6 Find dom R…

A: Here, the domain of R(t) is nothing but an intersection of the domains of each term. Domain of…

Q: (c) Let vector Ğ be given by Ğ = (2xz)i + (x²/2)j - (z²)k. Calculate the divergence of G.

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Q: FIND THE DIVERGENCE OF THE VECTOR F GIVEN = sin (8x)i + cos (5y); + z ² k FIELD F(X, Y, 2) BY

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Q: A scalar field is given by f = x2/3 + y2/3, where x and y are the Cartesian coordinates. The…

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Q: Q2. If F = (x² − y² + 2xz)ī − (2xz − xy + yz)j + (z² + x²)k, find the of curl F and curl of curl F…

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Q: Find curl F for the vector field at the point (9, -9, 5). F(x,y,z) = x²zi - 2xzj + yzk curl F =

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Q: Let F1 = (x+ y)Âx + (-x+y) ŷ– 2zî and F2 = 2 yx+ (2x +3z) ŷ +3yî. Calculate the curl and divergence…

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Q: Find the divergence of the field F. F = 8x 5 i + 3y 5 j + 2z 5 k 8x4 + 3y4 + 2z4 O 40x4 + 15y4 +…

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Q: Find the divergence of F(x, y, z)= x î+y³ ₂² 7 +xz³ k. O1+3y²z²+3xz O1+3y²z²+3xz² 01+3y²₂² O 1

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Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (9, -9, 9)

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Q: Evaluate the limit of the given vector-valued function: lim,o cos 2 + In(t + 1)j + ek| 12 O The…

A: We have to find the limit: limt→0 cos 2tt2i^+ln(t+1) j^+e-t k^

Q: Show that whether the functions sint and cost in the vector space C[-n, 1]of continuous functions on…

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Q: 2. Find the limit of the following vector functions: а) lim (2eti + 6e-tj – 4e-2tk) t→ln 2 b) lim i…

A: We have to find the limit

Q: curve in the xy-plane is denned by the vector valued functic dy in terms of t? dx? where x(t) = 2…

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Q: let 2 Vector tield A=x B=y2 Find explicit expresom of Lie derivative L, CB)

A: Please find the answer in next step.

Q: Is the vector valued function continuous at t=3? Defend your answer. I² -9 t- 3 V3t – 1, In(4 – t),…

A: Topic = Continuity

Q: 4y The divergence of the vector G = i+ sin y j+ 3k is :- -8y + cosy x3 الخيار 2 O

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Q: If F = (x² − y² + 2xz)i + (xz − xy + yz)j + (z² + x²)k, find the divergence of - curl F and curl of…

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Q: Let R be a vector-valued function defined by VA -1, , In(t + 1) sin 3t if t+0 (2, 3, 0) if t= 0.…

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Q: Let f = (r +2ryz)i+( + 2xy)j+ (+ 2xyz)k. Find j at (1.0, 1). (a) divergence of

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Q: Find the directional derivative of the field f(x, y, z) = -4x³ + 3 xy² + 5 y³ at P = (-1,–3,5) in…

A: Given f(x,y,z)=-4x3+3xy2+5y3  we have to find directional derivative of f at P=-1,-3,5 in the…

Q: 5. If a vector function F depends on both space coordinates (x, y, z) and time t, show that dF = (dr…

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Q: Find the divergence of F. F(x, y, z) = 8xi + 8y²j + 8z²k

A: Given,           Fx,y,z=8x2i+8y2j+8z2k

Q: Find the divergence of the vector field F = < yx², xz", zy® div F II

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Q: 3) Find the divergence and curl of f3xi+ 5x} j + 2y²k, at the point (1,2,3)

A: Solution is done in step 2

Q: ƏF dF = (dr. V)F+ -dt. at

A: Given: A vector function F depends on both space coordinates x, y, z and time t.  To Find:  To show…

Q: Vt-2 lim (vt – 3, (;) tan t→4 t-4

A: Given that the vector valued function and we need to find the limit of the following vector – valued…

Q: Find the divergence of F. y F(x, y) 2 x* + y x* + y

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Q: If f(x,y) = x^3+y^3, sketch the gradient vector field: \grad{ f(x,y) }

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Q: Consider the vector space of continuous functions over the interval [-1,1] with the inner product…

A: Given that,

Q: d) must be done using Vector Calculus and the Lagrange multiplier. Optimize: the function f(x, y) =…

A: Given: The function fx,y=49-x2-y2 subject to the constraint x+3y=10. To optimize the function we'll…

Q: Find the limit of the vector-valued function if it exists. lim(e² i + sin(t)j + e¯¹²k) O does not…

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Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi - 2xzj+yzk; (9,-9, 9) curl F…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.