Q4: Calculate the integral , F.dr where F 2xy i + x'j, if the curve e, lying in the plane XY, is: (a) The segment of a straight line between the points A(0, 0) and B(1,2) (b) The polyline A(0, 0)C(1, 0)- B(1, 2). (e) The fragment of the parabola y= 2x' between the points A and B.

Q: Evaluate the line integral [[(3.ry² + 6y) dr, where C' is the path traced by first moving from the…

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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: Find a function y = f(x) that describes the parametric x = -2t + 1, y = 3t², for – o <t < ∞. curve

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Q: Evaluate ʃC F dr where C is the parabola y = x2 from (0, 0) to (2, 4) and F (x, y) =&lt; −ysinx,…

A: Given a curve C is a parabola from (0, 0) to (2, 4)

Q: Find a point on the surface x+4y--z² =1 where the tangent plane is parallel to the plane x+4y- z =…

A: we need to find gradient of given surface to know about direction of normal vector to tangent plane

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 8 n = 4 (-x¹ + 22x³ -…

A: (a)How large should n be to guarantee that the Trapezoidal Rule approximation  to is accurate to…

Q: 2. Find the equation of the tangent plane to the surface x²+3y²+4z² = 20 (2,2, 1). at the point

A: Step 1:To find the equation of the tangent plane to the surface x2+3y2+4z2=20 at the point (2,2,1),…

Q: For the line that has the equation X1 + 2X2 = 10, will pass through: %3D O (5,4) (10,1) O (2,4) O…

A: Given that  The equation of a line is x1+2x2=10 To find a point that will pass through the given…

Q: 4. Consider the curve in the plane defined by r3+y3 = 6xy. %3D (a) Find for any point (r, y) on the…

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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: Find the slope of the tangent line to the curve of the intersection of the surface x² + y² +2²= 9…

A: The tangent is the line that just touches the curve at a single point. In this problem, the curve is…

Q: SHOW COMPLETE SOLUTION, MAKE THE SOLUTION CLEAR. THANK YOU!

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the equation of the plane tangent to the graph of z + xyz = 33 at (1,2,3).

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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: 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: 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: a) y = x' – 9x?

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the equation of the tangent plane to the surfaceln(x3 + y3 + z3) = x2z + 1at the point (1, 1,…

A: The objective of this question is to find the equation of the tangent plane to the given surface at…

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: 4. Let 0 ‡ b, c E Rn and define A = be E Rnxn. Show that (a) R(A) = span{b}, (b) N(A) = {x ≤ R" |…

A: (a) We are given that A = bcT                    where, c ∈ Rn     So, R(A) = { Ax : x ∈ Rn×1 }…

Q: Suppose you head toward the xy-plane from the surface x? + y? – 2² = –1 at the point (1, 1, v3) by…

A: given,     x2+y2-z2=-1 at the point 1,1,3

Q: Cis the semicircular curve drawn in the ground (the xy-plane) joining the points (0, - 2), (2, 0),…

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Q: Solve ut + cux=et, u(x,0) = u(x). Draw the characteristics in the x-t plane.

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Q: Let F(x, y) = (x + 1)j, and let C be the portion of the parabola y = x² that starts at (0,0) and…

A: The integral ∫CF⇀.dr⇀ is positive. From the graph the angle between direction of F⇀ and dr⇀  is…