Find (1) (ii) F(x,y) dy F(x, y) ds where F(x, y) = 1 and C is the curve y=x²-Inx from (1,2) to (2,2 – In 2).

Q: Find the point where the tangent line to the curve 7(?) = (V? +3,ln(?² +3),t) at (2, In 4,1) 5. %3D…

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Q: 21 Let F(x, y) = (3x + 2y)i + (2x - y)j. Evaluate F. dr where C is the curve X y from (0, 0) to (1,…

A: Here we calculate the integral along the curve x = y2 from (0,0) to (1,1)

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: Evaluate (2x-y)dx+(x+3y)dy along the path C: curve on y = 1-x² from (0,1) to (1,0).

A: Given the line integralI=∫C(2x−y)dx+(x+3y)dyCurve y=1−x2

Q: (a) Compute the directional derivative of f(x, y) = xy² + x³y at the point (4, -2) in the direction…

A: Since you have posted independent questions, so these are considered as multiple questions.According…

Q: x(t) = t², y(t) = t³ – 3t, on – ∞ <t < ∞ %3D а. Show that the parametric curve has two tangent lines…

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Q: (5) Find the equation of the tangent plane to z = 1² + xy +3y* at r = 1, y = 1.

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Q: Suppose the two curves r(t) = (t,0, 1 + e' sin(t)) and q(s) = (0, s, vs² + 1) lie entirely on the…

A: According to the given information, consider the given two curves:

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: Consider the function f(x, y) = x² + y² — xy. >) Find the equation of T(1,0), the tangent plane at…

A: Given: A Function fx , y=x2+y2-xy. To Find :  a) Equation of tangent plane at the point x=1 , y=1.…

Q: a) Compute the gradient of the function f(x, y, z) = e*y² . b)Compute the directional derivative Daf…

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Q: Let (t)=(-5t2+4,t³-+4,2+³) 7 Find the line (L) tangent to (t) at the point (-1,0,2) L: (x,y,₁2)= +t

A: The given problem is to find the line tangent to the given parametric curve at the given point…

Q: Find an equation (x(t), y(t), z(t)) of the line that is the intersection of tangent planes at (1,…

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Q: C is the curve y = e® from (2, e²) to (0,1) and F = (x², -y), compute ſ, F-dr.

A: Given that, C is the curve y=ex from 2,e2 to 0,1 and F=x2,-y Then, F=x2,-y=x2,-ex So, F→=x2i^-exj^

Q: Consider the curve C defined by (x; y) = r(t), where r(t) = (t; (1+t)/t; (1-t^2)/t) ; t > 0: (a)…

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Q: . Evaluate SF.dr: ▪ F = (x+z)i +zj+yk. C is the line from (2,4,4) to (1,5,2).

A: Since all subparts are different and not interlinked so as per our guideline we are supposed to…

Q: Evaluate S (xy + x + 2) ds along the curve r(t) = 2ti + tj + (3 - 2t)k, Osts 1.

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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…