5) Suppose a path C is defined by r(t), 2 and r(8) = < 6, 10 >. If f is a differentiable function satisfying f(3,9) = 6 and %3D f(6, 10) = 14, what is the value of Vf ·dr?

Q: Then, the only positive equilibrium point of Eq.(1.1) is given by (2.7) (1 – A) (E Bi) Li=1 provided…

A: Given linearized equation of Eq(1.1) about y~ takes the form ;…

Q: 1. Let f(x, y) = In(x - y) then at the point (4,1), fryis equal to: %3D -1/9 O 1/7 1/9

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 7-The tangent of the curve x^2+y^2- 2xy3D0 at the point (1,1), is * O a. y=2-x. O b. y=x-2. C.…

A: We find equation of tangent to the curve

Q: 16. Of all points (x, y, z) that satisfy 3x + 4y + 2z = 52, find the one that minimizes (x – 1)2 +…

A: Let f(x,y,z)=x−12+y−42+z−22   and    g(x,y,z)=3x+4y+2z−52≡0Apply Lagrange Multiplier method to find…

Q: 2. Compute F-dr where E= (x+ y,x-2z,z- y) and curve C is the line segment from (-3,5,1) C to…

A: Using line segment as the base of a rectangle, we choose the height to be the height of the surface…

Q: 18.7. Let f(z) = (e + e-2)/2. Evaluate f(2) -dz, where y is any %3D simple closed curve enclosing 0.

A:

Q: 2. Let f(x, y, z) = In(x² + 2) + y²e#* - cos(2yz). Find fzyz-

A:

Q: Which of the following is a parameterizatino of the line that passes through the point (5, 4) With a…

A: Let's find.

Q: Then, the only positive equilibrium point ỹ of Eq.(1.1) is given by Ei-1 di = (2.7) Li=1 provided…

A: We have a function H defined as Hu0, u1, …, u5=Au0+∑i=15αiui∑i=15βiui which implies that H is the…

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A:

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A:

Q: The first provider can provide at most 5 tons, and the second one at most 3 tons. Finally, in order…

A: (2): Given equation is x≥2y-1 Draw the diagram of domain P

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A:

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A: In the question it is asked to find the path of a heat-seeking particle placed at point P. Given:…

Q: The nature of the stationary point (0, -1) for the function f(x,y), if f= 4-12x, fy= 0 and fry=-4+…

A:

Q: Let xo E (0, o0) be the value ofx E (0, 0o) that minimizes the function f: (0, co)R defined by f(x)…

A: The given function is fx=x2+x-2. the graph of the given function is, Clearly it is not defined at x…

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A:

Q: (A) Evaluate fz dz along from z 0 to z-4+i along curve of c given by the line from z-0 to z= 2i and…

A: Let's find.

Q: If (1,1) is a critical point of f(x,y) = x³ – 3x + 3y² – 6y then (1,1) is:

A: (1,1) is the local minimum point   explanation is given in below step

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A:

Q: Compute analytically convolution of x(t) and h(t) defined as follows: S 1, if 0 <t< 2, { 0,…

A:

Q: An object is moving along a path defined by the graph   x2+y2=2   Compute dy/dy, if dx/dt=2,x=−1,…

A: Differentiation application

Q: 2.2 11, IfF = xyz\+x*y°z}+ xyz k then find div F at (2, 1, – 3).

A:

Q: 7. Which of the following is the potential function for F = (2ху + 1,х2 + 2yz, y? — 2)? а. Ф(х, у,…

A:

Q: Given the one-parameter family of curves y² = Cx³ + 5. Find the family of orthogonal trajectories.…

A:

Q: 27. Consider the piecewise path which goes along (t,3 – 3t, -t) for 0 <t<1, then along (1,t,-1+ t)…

A: Line Integral along the given parametric curve.

Q: 2.7 Given that the spacial components of motion, x = x(X, (), are: x₁ = X₁ + X₂ (e' - K), X₂X₁…

A: Solution : x1=X1+X2(et-K)      …(1) x2=X2+X1(e-t-K)   …(2) x3=X3    …(3) Solving above equations,…

Q: ,7. Find the four second-order partial derivatives for f(x, y) = 9x°y° + 6x'y 8,6 Txx %D fy %D Txy…

A: Four partial derivatives are given below

Q: Let C be the shortest path that connects t to ni and I = J. (coshz + 1)dz. Then %3D O I=-1-cosh t+…

A: Since you are asking multiple questions. We are answering only the first questions. Let C be the…

Q: 3.5 Given that H = x'a, + ya,, evaluate H· dl, where L is along the curve y = x from %3D (0, 0) to…

A:

Q: 5) Show that to order O(h²), the central difference formula for the partial derivative მ3u(x,t) əx3…

A:

Q: If Z = x + iy than Z is: Z = x - iy Z = -x + iy Option 3 Option 2 Z = x + iy Z = -x - iy Option 4…

A: Explanation of the answer is as follows

Q: If f(x, y, z) = 2 sin(100xy) In(2), compute the value of the limit f(1, h, e) – f(1,0, e) lim h→0 h

A:

Q: Find valume bounded by abave Z:4-20 and below by Z-xy 2.

A:

Q: Let f(x, y, z) = In(x² + z) + y²e#². Find fzyæ-

A:

Q: {x} € 1, Show that property (3) of a matroid implies: For any S e there exists y € S, such that S \…

A: Following is the definition of a matroid. A finite matroid M is a pair (E,?), where E is a finite…

Q: Let C be the shortest path that connects t to ni and I = S. (coshz – 1)dz. Then |=-sinh n+ n(1-i)…

A: The solution is given by using line integral method as follows

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A: In this question we will use basic of calculus i.e concept of vector calculus. We will find the…

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A:

Q: (5) Suppose that A = {(x, y) = R²|x² + y² = 0 or 1 < x² + y² ≤ 4}, then (1, 1) is ( (B) accumulation…

A: Given A=x,y∈R2|x2+y2=0 or 1&lt;x2+y2≤4. We have to find the correct answer among the given options.…

Q: 5) a) Compute Ko for the function f0=V+X by using the de finition of the deniratire, b) Find the…

A:

Q: Find the value of k that makes function continuous at z=4 |2z + 6 z> 4 5z – k z< 4 f(z) = ualuo…

A: Continuity.

Q: A clamped cubic spline for a function f on 0,3 is given by [1+ax² -2x', S(x) = . [1-2(x-1)+b(x-1)² +…

A:

Q: 4 Suppose that f(x, y) = x* + y* – xy Then the minimum is 0

A: Disclaimer: Since you have asked multiple questions we will solve the first question for you. If you…

Q: If y(x) is a solution of y' = (y+1)(50 – y) with y(0) = 0, what is the limit of y(x) as x approaches…

A: Given: yx is a solution of y'=y+150-y. Also, y0=0. To find the limit of yx as x→+∞. As, y'=y+150-y.…

Q: Find a parameterization for a line passing through the points (0, 0) and (2, 8) O x=t, y = 4t Ox=t,…

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Q: Suppose f has partial derivatives f,(x,y) = 3x-y and fAx,y) = 4y - x- 1. Classify each of the…

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Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2 = c^2. *

A: Curves:  x²+y²=c²