Use Green's Theorem to evaluate C F.dr, • dr, where F = (√x+5y, 4x + √y) C consists of the arc of the curve y = 1x (0,0) to (1,0) and the line segment from (1,0) to (0,0). 1x - x² from Hint: Check the orientation of the curve before applying the theorem.

Q: find the distance from the point P (2,1,1) to the lins x+1 y-1 Z-3 L: 6 -2 -3 = =

A: To find the distance from the point to the line.

Q: 3. Sketch the curve: y = (x²–1)(x+2) x-3

A: y=(x2-1)(x+2)(x-3)y=(x-1)(x+1)(x+2)(x-3)X-intercept:(-2, 0), (-1, 0), (1, 0)Y-intercept:(0, 23)…

Q: (b) Sketch the graph of the function y = 1+ /16 – x²2 for -4 < x < 4. Hint: x2 + y? = 16 is the…

A: Consider the equation of the circle The graph can be plotted for the circle as

Q: Evaluate Szdz where y traces the arc of the parabola y = x² from (1,1) to (2,4).

A:

Q: Find the tangent plane to the equation z = 2x² 2= 56x-430y + 1554 X 2x²2y² + 4y at the point (3, 4,…

A:

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

A:

Q: Prove that the tangent lines to the curves 5y – 2x +y³ – x²y = 0 and 2y + 5x +x* – x³y2 = 0…

A: Given: - The statement is, The tangent lines to the curves 5y-2x+y3-x2y=0and 2y+5x+x4-x3y2=0…

Q: If a half-turn centered at F(3,7) is applied to the point A(9,12), what are the coordinates of its…

A:

Q: Evaluate fF dR given that F(x, y) = 2yî + (xy – 2x)j and C is the curve in the third quadrant from…

A:

Q: Evaluate A = F. dr where F(x, y) = (6x – 2y)i+x²j for each of the following curves. a) C is the line…

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Q: Let y = f(x) be defined parametrically as y=t+tt, x = 2t -t, te R. Find f(x) and discuss its…

A:

Q: Prove that the curve y: (-,-)→ R³ is regular with factor H and determine whether the image y (t) =…

A: If γ't not equal to 0 for all t∈-π2,π2then it is regular. If γ''t=kγ't for all t∈-π2,π2 then the…

Q: Find the tangent plane to the equation z = z = 16x + 15y + 19 X - 2x² + 3y² - 3y at the point…

A:

Q: -5 -4 -3 -2 -1 n y = دیار 2- 7 1 -2- -3- -4 2 3 4 10 5 Write an equation for the function graphed…

A: Given graph

Q: Verify Stoke's Theorem for F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1…

A: Given: F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1 and z² = x² + y².

Q: c. Evaluate f 3x ds, where C consists of arc C₁ of parabola y = x² from (0,0) to (2,4), followed by…

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Q: Suppose that a curve is given by the equation y2=x2+x+1 which defines y as function(s) of x Find…

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Q: Determine the equation of the tangent to the graph of y- x - 3x + x+3 at the point (- 1, -2). O a)…

A: We have to find the tangent of the given function at point (-1,-2).

Q: Consider the folloinwg curve: y = square root of -1+2x At what point on the given curve is the…

A: Consider the folloinwg curve: y = square root of( -1+2x) to find the point on the given curve is the…

Q: Evaluate the length of the curve: y = 3x + sinx, 0 ≤ x ≤ 1.

A: Let L be the length of curve  F(x) = 3x + sinx