Question 16 Given fx.y) = -e-x - 3x a) f,(0,0) is equal to b) f,(0,0) is equal to c) Using the linear approximation L(x.y) of flx.y) at the point (0,0), an approximate value of is equal to

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A: Given function is At origin,

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Q: The linear approximation for f(x,y)=Vy+cos?(x) at (0,63) is O L(x.y)=(65+y) 16 L(x,V)=(65-y)

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Q: Prove that A <m AUB where AUB = {0x | r E A}U{ly|y € B}.

A: Solution: Let us consider two sets A and B. It may be possible that A∩B≠∅. But we want to construct…

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A: We have to find the value of given line integral.

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Q: Given etye -Z+ xy - e-0, use e =0, use impicit partial denvatve to finid 2ž at the Point (1 2t

A: Explanation of the solution is given below....

Q: IV. Bosqueje la región en el plano que consiste de todos puntos cuyas coordenadas polares satisfacen…

A: We are authorized to answer three parts at a time, since you have not mentioned which part you are…

Q: If u = x°f(x/y) according to Euler's theorem xUx + yuy is 5u %3D

A: given that u=x5fxy verify whether xux+yuy=5u is true or false

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Q: Question 6 Evaluate the line integral √3xy ds line Segment Joining (-5,7) to (3,1) where is the

A: First we will parameterized the equation of given line segment

Q: If C is the line segment from (1, 3) to, (0, 0), find the value of the line integral: 3y i+ 3x j) ·…

A: Given If C is the line segment from (1, 3) to, (0, 0),

Q: The path integral v- dr, where v = (sin y, x - cos y) and C is the perimeter of the triangle formed…

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Q: du If u = x²y + y²z + z?x then at (1,1,0) is ax %3D -

A: Given that u=x2y+y2z+z2xTo find :∂u∂x  at 1,1,0Solution :u=x2y+y2z+z2x∂u∂x=2xy+0+z2∂u∂x=2xy+z2

Q: If C is the line segment from (1, 3) to, (0, 0), find the value of the line integral: So(3y² i +3xj)…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 2. Evaluate directly the line integral fo a dy where C is the quarter-circle from (0, 4) to (4, 0)…

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Q: r 64 In(y) 49 VY

A: We need to solve definite integral.

Q: Exercise 4.3.8 Show that if A = E oiu;vf , then At = Ei=1 0,'v¿u

A: Given function is, A=∑σiuiviTi=1r As we know that, A+B+=A++B+ So, we can write the above equation…

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Q: 7 Prove : id Is perpendicular line to ra duic at its outer end point ,then t ang ent to the cirde is

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Q: Solve by theorems of linearity and translation. f(t) = cos t + sin t

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Q: The value of the line integral | F(r).dr when C F(F) = [-y, -xy]and C is the upper half circle arc…

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Q: find ow/ar if w = (x + y + z)², ar www w x = r – s, y = cos(r + s), z = sin(r + s) at the point (r,…

A: See the attachment

Q: Is AB a tangent to OC? 29 C 10 A Your answer: nt o Yes, AB is a tangent. No, AB is not a tangent.…

A: We have to check

Q: Q1: - Find Ow/Du and Əw/Əv if w- xy + yz + xz ,x-utv, yru-v,z-uv at the point (u,v)- (0.5,1) (30…

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

Q: Evaluate x*dx C + xy dy, where C is the triangular curve consisting of the line segments from (0, 0)…

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Q: (b) Apply the method of contour integration to prove that (2m de 2n Jo 2+cose 3

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Q: If C is the line segment from (6,3) to, (0,0), find the value of the line integral: Se(by? i+ 3z) -…

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Q: sphere will reach point B as it swings about 'O' (a) If OA is a rope vertical plane. Determine the…

A: Answer:

Q: 2.lexPress the faiauing curve inthe form of Yara meter eQuation al Y=1-×モン-2 b.) y? zzg,x>4

A: Solution given below

Q: The equation of the tangent plane to the surfice. -yeV + = 0 at the point (0,1,1) is ar + by + cz =…

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Q: 5. Find the equation that gives the FT of x,(t) * x,(t) * x,(t) where x,(t) is the rectangular pulse…

A: It is given that

Q: 2л where a, b > 0. dx = - ile* + b Prove that %3D

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Q: 1. Evaluate the given line integral, | (2² – y,y) · dŘ, where C is the part of a = y? – 1 from (0,…

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 2. Evaluate the given line integral, (-y, x – y) · dR, where C is the line segment from (2,0) to (0,…

A: Using parametric equation, line integration is evaluated.

Q: The equation of the tangent plane to the surfae ye+ = 0 at the point (0,-1, 1) is az+by+cz = Which…

A: Given yexy+z2 = 0    point (0 , -1 , 1)Let f = yexy+z2dfdx= yexy.y ⇒dfdy(0 , -1 , 1)=1dfdy= yexy.x…

Q: In the text we obtained the result (Vx F) = F, OF, ду C3 P (Xp, yo, 0) by integrating over a small…

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Q: A string of length 1m attached with two points. The deflection in the string is given by y" + Ay =…

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Q: . The uejveciion of a beam is governed by the equation d'y + 81y = 0 (x) dx %3D where o(x) is given…

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Q: 5. Show that the equation of the tangent plane to f(r, y, z) = c at (ro, Yo: 20) is given by the…

A: This is the question from vectors.

Q: (b) Evaluate (3, 10) J(0, 1) Cto (3x + y) dx +(2y - x) dy along- @ curve y= x? +1; (ü) the line…

A: Given function is 3x+ydx+2y-xdy i) Given curve is y=x2+1 Hence the integrand becomes…

Q: The path integral fv· dr, where v = (sin y, x – cos y) and C is the perimeter of the triangle formed…

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Q: If C is the line segment from (8, 1) to, (0,0), find the value of the line integral: Se(8y² i+x3) ·…

A: First we have to write the equation of the line segment C and then convert the given line integral…

Q: Note: Answer either Yes or No or Not-Applicable in the block provided. Consider the DE ry" – y' +y =…

A: We will find out the required values.

Q: a) Evaluate the line integral S. (2x - y) dx – (x + 3y) dy, where C is a straight line from (1,1) to…

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Q: Given observations (xį, Yi), i = 1, … n, fit a quadratic sion model Yi = f (xi) + €i, where f(x) = a…

A: The polynomial equation that will fit is y = β0+β1x+β2x2+....+βrxr to the n pairs of observations…