1 3. (8 points) Evaluate the contour integral dz where C' is the counterclockwise oriented curve | z − 1 |= (z²-2z) 2.

Q: Evaluate [F·dr if F(x, y)=(4e³)ī +(4xe³)j and the curve C' is line segments going from (0,0) to…

A: To evaluate ∫C F⇀·dr⇀ if F⇀x, y=4eyi⇀+4xeyj⇀ and the curve C is line segments from 0, 0 to 5, 4 to…

Q: 13. Find an equation for the tangent plane of the graph of f at the point (xo, yo, f(xo, yo)) for:…

A: Note:-Since you asked multiple questions which are not interlinked to each other, according to our…

Q: |(x+2) ds, where C is the curve represented by: r() = ti+*j+;rk, -Evaluate 0sIS2.

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Q: 'ind parametrizations (a) The line from (a, b) to (c,d). (b) A path from (2,0) to (0, −2) along a…

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Q: 2. Evaluate f (x^²y³ − 2y)dx + (3x + x³y²)dy where is the curve given below oriented in clockwise…

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Q: ve = Vti + Vrj + (2t – 1)k is tangent to the surface x+y-z = 1 Show that the curv when t=l

A: Consider the given curve r=ti+tj+2t-1k And the given surface x2+y2-z=1 First, write the curve in…

Q: 6.(6 pts) Evaluate the line integral / (x+ y + 2) ds along the curve C given by r(t) = (sin t, cos…

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Q: 6a) Let A be the parabolic arc defined by the equation y = 8x – x´ over the domain interval [0, 8].…

A: (a) Consider the given function. y=8x-x2 Now, draw the above function by using the calculator.

Q: F(x, y) = x² i + y² j C is the arc of the parabola y = 4x² from (-1, 4) to (0, 0) %3D (a) Find a…

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Q: Consider the tangent line to the curve r(t) = t2i −(1/(t + 1))j +(4 − t2)k at the point P(4, 1, 0).…

A: Given the tangent line to the curve r→t=t2i^−1t+1j^+4−t2k^  at the point P4,1,0. We have to…

Q: Which of the following is/are points on the curve y-x Br+ 22x - 24x +9 whore the tangent line is…

A: We need to find the points on the curve where the tangent line is parallel to the x-axis.

Q: Let C be the simple closed curve which consists of the line segment from (1,1) to (-2,4) followed by…

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Q: Evaluate [ f (x,y,z) ds given that f(x,y,z) =, and the curve C is ř(t) = 2ti +t²j+÷tk (1<t<∞) %3D…

A: Given: f(x,y,z)=x2xy+6yz r→(t)=2t i→+t2 j→+13t3 k→   1≤t&lt;∞

Q: Let C be the curve connecting (0,0,

A: Given that C be the curve connecting  (0, 0, 0) to (1, 4, 1) to (3, 6, 2) to (2, 2, 1) to (0, 0, 0).…

Q: The functions g(b, c, d) and h(b, c, d) are defined as: g = (b+ c+ d')' + (b' + c' + d') · (b' . c'…

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Q: Ev 2 x 2 [x²z dx - yx² dy + 2 dz along the curve C'shown in the figure. AZ 2

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Q: Let F=-yi+xj and let C be a curve consists of the line segment C₁ from (0,0) to (4,0) followed by…

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Q: 99. Determine the concavity of the curve x= 2t + In t, y = 21 – In t. %3D

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Q: 13. Find an equation for the tangent plane of the graph of f at the point (xo, yo, f(xo, yo)) for:…

A: Note:-Since you asked multiple questions which are not interlinked to each other, according to our…

Q: Let P be the tangent plane to the graph of g (x, y) = 20 10x² - 20y² at the point (4, 2, -220). Letf…

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