If F = 3xyi - y²j, evaluate [F.dr where C is the curve in the xy plane, y = 2x², from (0, 0) to (1, 2).

Q: Q.7: find the directional parametrization of the line segment joining two point A(2,1,3) and…

A: It is a basic questions of 3-D geometry , we have equate the equation only

Q: Evaluate √(2² + yz sin(xyz))dx+(y²+xz sin(xyz))dy+(x+xysin(xyz))dz where C is the curve following…

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Q: a) Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y - 2y³ In…

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Q: Q2) Find the T „N of the vectors curve r(t) = at the point (1, 1)

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Q: ind the equation of the plane tagent to the curves f (t) = [3t+4,4 tº, sin (πt) + 4] and g(s) = [8°…

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Q: Compute F. dr for the oriented curve specified. F(x, y) = (4x2, xy), line segment from (0, 0) to (2,…

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Q: Evaluate where F(x, y) = x² i+(y² – x) j and C is the line segment from (2, 4) to (0, 4) followed by…

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Q: nd the tangent plane to the equation z = a? – 4y? – 2y at the point ( – 3, 3, – 33)

A: In this question, concept of tangent  is used. Tangent A tangent is the line that runs parallel to…

Q: Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y-2y³ In the…

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Q: equations

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Q: hat is the scalar equation of the xy plane?

A: Given query is to find the scalar equation of the XY plane.

Q: Find the equation for the tangent plane to the surface -3x+ 9y -7z = -26 at the point (1,-1, Lütfen…

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Q: tangent plane

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Q: 8) Given z =f (x.y) =1- (x² +4y2) ,Find : a)The vector function, 10 normal to the surface of f at…

A: This is problem of vector calculus.

Q: Find the distance between the point (0,0, 8) and the plane given by 2x – y + 2z – 1 = 0.

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Q: Given the function z = In(x - 2y), find the equation of the tangent plane when (x, y) = (3, 1) in…

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Q: OShow that every point (b, c) in the plane lies on a tangent line to the graph of y = x³.

A: Consider the given information. y=x3 Find the derivative of the function. dydx=ddxx3y'=3x2

Q: A fire ant, searching for hot sauce in a picnic area, goes through three displacements along level…

A: Since you have posted multiple questions. I am answering the first three sub-parts. Please post the…

Q: Consider the curve F(t) that represents the intersection of the surfaces x + y? -1=0 and y= 2x a.…

A: Given: The curve r(t) represents the intersection of the surfaces x2+y2-1=0 and y=z/2x.

Q: Let C be the curve in the x-y plane defined by the equation (x – h) + v – k)* =? where h, k, and r…

A: Equation of the curve is x-h2+y-k2=r2 & a, b is a point on the given curve. a). Slope of the…

Q: Let r(t) = (-5t³ – 1, t² + 5t³, 3t²). Find the line (L) tangent to (t) at the point (39, -36, 12)

A: r→(t)=⟨−5t3−1,t2+5t3,3t2⟩Find the line (L) tangent to r→(t) at the point (39,−36,12)

Q: Let P = (1,3) and Q = (2,6) be points in the plane. Find a vector-valued function R(t) = R0+tv such…

A: Consider the given points: