Find the line integral where C is the semicircle y = A. I = 96 B. I-160 80 162 traversed from (4,0) to (-4,0). Jo (3x - 5y) ds,

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Q: Parametrize the osculating circle to y = √x at x = 4.

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Q: - Find div F and curl F if F(x, y, z) = 10y¹z7i – 17xªzºj – 3xyễk. div F= curl F=

A: The general form of a vector-valued function in three dimensions is given by F=F1i+F2j+F3k, where…

Q: zy² z²+1 Round your answer to four decimal places. Find -dA, R= [0,3] × [-4,4]

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Q: If X = U+v , y =U-V then Show that + 2 du? = 2) ( %3D nene Than ded uce that wok cu+ v*+ (u+v) g…

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Q: Evaluate (2x - y) dx + (x + 7y) dy. C C: x-axis from x = 0 to x = 2

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Q: Eliminate the constant: =c₁e²x+c₂e³ 3x

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Q: Ir th line x=4+2t, ーも paralled to the plone 3x +ry +2=7-

A:

Q: Q.2 Find DivF and curlF at point (1,2) , where f(x, y) = xy² + Inxy

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Q: Determine the magnitude and direction of the largest change 2 2 (x² + y²)z at the point M (1, -2,1).…

A: Introduction How sharply a curve rises determines its magnitude. It is simplest just examine the…

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Q: Consider Flx,y) = (3x2 +6y) i t (6x +4y%)j. (as Show that Fis lonservative a function Such Line…

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Q: Calculate the imaginary part of  ∮C(Re(z)+3.43)(1z^2+9z+11 / z)dz  where C:|z|=1  Use FOUR…

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Q: Calculate the imaginary part of  ∮C(Re(z)+3.78)(2z^2+ 5z+ 13 / z)dz  where C:|z|=1  Use FOUR…

A: We have to find the imaginary part of the integral ∮ fzdz, where fz=Rez+3.782z2+5z+13z over the…

Q: Find curlF for F = xyz?i+ x*yz?j+ x*y?zk.

A: Given, F→=xyz2i→+x4yz2j→+x4y2zk→ Used formulas, ∂∂xxn=nxn-1

Q: Explain the geometric meaning of r'(t).

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Q: ſx = s² – t² . z = 2x – 5y, ly =s•t³ · t3

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Q: xxx, xy(Rxy →→~Ryx) - vx~Rxx

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