19. Evaluate Scx ds, where C is a. the straight-line segment x = t, y = t/2, from (0, 0) to (4, 2). b. the parabolic curve x = t, y = t², from (0, 0) to (2, 4).

Q: By using Green's theorem evaluate £ (Ary – y") dr + (** + 3ry) dy where C is a closed curve starting…

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Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

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Q: Use Green's theorem to evaluate , (5xy + x2 + y?) dx + (x²-y)dy where C is a closed curve that is…

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Q: Evaluate x ds, where C is a. the straight line segment x =t, y =. from (0,0) to (6,2) b. the…

A: We need to evaluate ∫Cx ds

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A: We have to solve the given integral by Green's theorem.…

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A: The tangent plane to the surface is a plane that only touch the surface at the point.

Q: 13.3. Let y be the curve given by z(t) = t + it?, 0<t < 2T. Evaluate |z|²dz.

A:

Q: 2. Prove that the following curves are intersecting with a right angle: 5y-2x+ y –x*y =0 2y+5x+x*…

A: Given curves are  5y-2x+y2-x2y=0and2y+5x+x4-x3y2=0

Q: Evaluate [(x +2y) ds, where C is the curve defined by y = √√4 – æ², for x = [0, 1

A: Here ds is arc length.

Q: The length of the curve determined by equations x = t² and y = t from t = 0 to t = 4 is %3D %3D %3D…

A: The objective of the question is determine the length of the curve.

Q: d'y Consider the curve y = ry+ 1, What is the value of at (0, 1)? dz

A: Given curvey2=xy+1

Q: the detined b is Constant. Curiature a(t) =| 1 Cost, 1 sint, o of the curve d:laa)tR? where Find

A: We are given : α(t)=1rcos t,1rsin t,0 ⇒α'(t)=-1rsin t,1rcos t,0 Now, the Unit tangent Vector is :…

Q: 10. If the curves f(x, y) = 0, y, z) = 0 touch, show that at the point of contact, dr dø dr dø dy dx…

A: According to our guidelines, we can answer only the first question, the rest can be reposted.

Q: s Compute yz dz + zzdy + zydz along the curve (t, t2, t³), 0 st<1

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Q: Compute f ds for the curve specified. f(x, y, z) = xz, r(t) = (3e, 2v5t, 4e) for 0sts 1

A: Here the provided function f(x, y, z) of three variable and a curve C is defined. Then the line…

Q: If C is a piecewise smooth curve from (1,2, 3) to (4,5,6), then | . dx + 2 dy + 3 dz=

A: The value of the given function can be found with the help of the integration. Substitution of…

Q: What isfor the curve given by x = (t – 1)³ and y = vt ? | dx 1 2VE 6VE(t-1)2 3(t-1)2 O Option 4…

A: Using chain rule of differentiation

Q: 2) Consider the oriented curve C given by C = C1uC2, where C2 is obtained by intersecting the…

A: We will first parametrize the curves C1 &amp; C2 then substitute the x,y,z values into the line…

Q: r(t) = 6ti + 3/2ťj+2¢k, 0<t<1

A:

Q: If lx + my = 1 touches the curve (ax)" + (by)" = 1, show that %3D )+) = 1.

A:

Q: By using Green's theorem evaluate (4.ry – y') dr + (x + 3ry) dy where C is a closed curve starting…

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Q: Evaluate yz dx +y dy +a dz, where C is the line segment from (2,0, –1) to (4, 1, 2).

A:

Q: Calculate a 3 ydz t 13x'y dy, Where Cis the oriented curve given in the figure . 3 Bydr+43xy dy =?…

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Q: Consider the curve y = zy+1. What is the value of- dz at (0, 1)? None of the given choices

A: The solution for the above question is as shown below.

Q: 23. Evaluate x² c ¥4/3 ds, where C is the curve x = t², y = t°, for 1st< 2.

A: Given curve is

Q: Evaluate ∫C x ds, where C is the parabolic curve x = t, y = t2, from (0, 0) to (2, 4).

A: Given: Parabolic curve x=t, y=t2 from (0,0) to (2,4)

Q: Let C be the curve y = x³ – 3x2 + 4x – 1 joining the points (1, 1) and (2, 3). Find the value of…

A: We need to find value of integral.

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: By using Green's theorem evaluate £ (Ary – y) dr + (** + 3ry) dy where C is a closed curve starting…

A: Green's theorem in a plane: If D is a region inclosed by a closed curve C then ∮C u dx+v dy=∫∫D…

Q: If the equation of the tangent plane to x2+y2-147z²=0 at (1,1,/2 / 147) is x+ay+Bz+y=0, then a+ß+y=

A:

Q: If the equation of the tangent plane to x2+y²-83z2=0 at (1,1,/2/83) is x+ay+Bz+y=0, then a+ß+y=

A:

Q: |Verify that Green's Theorem is true for S,3(y2 – x) dx + (x² – y)dy given that the curve C is…

A:

Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

A:

Q: Find the length of the curve r(t) (1,t²,), 0sts1 %3D «3 Ost<1

A:

Q: s) Evaluate the line itegral ( +2y + 2)dy – dz, where C is the arc of parabola z = 2+ y". from (2,0)…

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Q: Evaluate + 5x)dx + (ye* – 3y²)dy where C is the boundary of the curve given below. -2

A: Detailed explanation mentioned below

Q: (is)Find the eguakion af the line tangent to y=ro* át (!,10')

A:

Q: If L is the tangent line to the curve 7 (t)= (2t-1, t, t-2) at (3, 4, 2) and the point where L…

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Q: a) Compute the equation of the tangent plane to the level surface 9(x, y, 2) = x’y + 2y°z – 3z°x = 3…

A: First we calculate gradient of g(x,y,z) at point (1,0,-1). Then find equation of tangent plane.

Q: What are the critical points for the plane curve defined by the equations æ(t) = sint + cos(t), y(t)…

A: Critical points.

Q: . Find SF dř where F(x,y,z) = (3y?e*, 6ye* -, 1+) and C is the curve F(t) = (sin t, ,2-) for 0 stsn.

A:

Q: Consider Gollow Sx2 of Eunluate y when y to Find y Evalnate of when 11 Write Mhe etios to the Write…

A: Now when x = 1, Now differentiating given equation with respect to x, we get Now when x = 1,

Q: py*(1 + x*)dx + 2ytan xdy ,where C is closed curve xi +yi = 1

A:

Q: What is the equation of the plane that is tangent to the graph of z = x coS y – ye“, when (x, y) =…

A: Equation of the plane tangent to the surface z=f(x,y) :               Let   F(x,y,z) =0 ,then…

Q: Show that the Bézier curve with control points Po = (1, 4), P = (3, 12), P, = (6, 15), P3 = (7, 4)…

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Q: 2) Find the cartesian eauation for the olar curve r=tan e sece ×ニy )yニxと 2.

A: