Evaulate the line integral of c (x^2+y^2) where c is the line segment from (-1,-1) to (2,2)

Q: Find the length of the curve r (t) = 3ti + square root of 3t^3 j + 2/3 t^3 k in [0,1]

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Q: If r'(t) = (1,21,3r*) and r(0) = (0,1,2) then r(t) equals %3D (a) (1,r°,r'). (b) (1,r",r')+ (0,1,2)…

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Q: B 4a X A 66° 20

A: The given figure is -  We have to find the value of 'x'.

Q: f(z) = (x+iy)^3 is analytic or not

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Q: D) Factor f (x) = x³ + 2x2 + 4x +8 into complex linear factors. %3D

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Q: (a) Suppose that k is an odd integer and w is a k-form. Show that w^w = 0. (b) Note: This question…

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Q: Assume that F= (e^x−y)i+ (2y−x)j, C1 is curve from (0,1) to (2,5) along the graph of y=x^2+ 1, and…

A: Given , F=ex-yi^+ (2y-x)j^ C1 is a curve from (0,1) to (2,5) along the parabola y=x2+1 C2 is a line…

Q: - If W = xy + y2+1 azw Show that a2w ey %3D дхду дудх

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Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: The equation x''+ x = sin t has a bounded solution. true or false ?

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Q: 1 1 1 1 ++* 1 2 1 1 -2 1 1 Which system of ODEs matches the velocity field above? Ox'= 1, y = x…

A: The velocity field is shown in the picture. Consider, x'=yy'=1 This means: y'x'=1yydy=dx Integrate…

Q: Linearization X = a [4 (b+y)

A: Note: As nothing mentioned about a and b, we will be taking them as constants in general. Further,…

Q: Which of the following are true for A = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 4), (3, 2),…

A: The given set .The given statement .The objective is to determine whether the statement is true or…

Q: f" > 0 on (-∞, -1) U (-1,0).

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Q: Let a be a real number and f(x, y) = 5ax?y+ 5xy³. Let v = 3i – j and let Vf(x, y) denote the…

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Q: at the point (In 12,2) Find the gradient for the function f(a, y) = y'xe # Find exact values. No…

A: The given function whose gradient is to be calculated at a given point is:

Q: if f(z)=u(x,y)+iv(x,y)=z^2+3z+4 find u & v

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Q: x^2y''-2xy'+2y=0; y1=x, y2=x^2 Verify that y1 and y2 are linearly independent

A: x^2y''-2xy'+2y=0; y1=x, y2=x^2 Verify that y1 and y2 are linearly independent

Q: a(t) v(t) r(t) = 2i+6tj + 12t^2k, v(0) = i, r(0) = 5j-6k

A: Here is the step-by-step explanation:We need to integrate the given acceleration function (a(t))…

Q: Compute ∫C(2x+√y)ds, where Cis the curve from (0,0) to (2,4) along y=x^2.

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Q: What is the smallest number that can be represented as the sum of four positive squares (not…

A: Consider the given statement. Since we need to find a number, which is the smallest number of sum of…

Q: The equations ry² + 8xzcos(u) + ye® = 16 and x³yz + xe" – 5u²v² = 15 are solved for u and v as…

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Q: Write a polynomial function of least degree with integral coefficients that has the given zeros. 23)…

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Q: Can someone help me explain why my teacher mutiplied the equation by (x^4)' in step 2? I thought I'm…

A: Given,

Q: 7. The function (x, y)= (2x* + y* )exp + xy' is homogenous in x and y of degree

A: .Given,f(x,y) = (2x4+y4) ey2x +x y3Put y= xSo we get,f(x,x)= (2x4+x4) ex2x +x x3 f(x,x)= (3x4) e0.5…