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Q: 3. Draw isoclines (include at least c = -1,0, 1) with their direction markers and sketch the curve…

A: Step:-1 Given differential equation is dydx=y+x2  with y-2=2 Part (a):-  Isoclines is a curve on…

Q: Let C be the closed curve indicated in the diagram. Use Green's Theorem (2,1) (o,i) (x² + y?, y³ +…

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Q: Let C be the curve y = 2.5 In (6.25 – x²), for – 1.2 < x < 1.6. A graph of y follows. 4.6 4.5 4.4…

A: Here, y=2.5 ln6.25-x2. So,         y'=2.5ln6.25-x2'           =16.25-x26.25-x2'    =2.5·16.25-x2-2x…

Q: 13- Find the length of the curve a) r(t) = 4costi + 4sintj³ + 3tk³ 0< t < 3n b) r(t) = 4ti + 4tj¬ +…

A: Please refer the image,

Q: 8. Show that the one parameter family of curves y² = 4k(k + x) (k E R) are self orthog- onal.

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Q: Find the exact length of the curve. v= In(1 – x²). y 0 <x < 1 In(|3|) - 8.

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: 2.2 Find upper bound of z + 4 -dz (z – 3i)3 + 1 where C is the circle |z – 3i| = 4.

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Q: Find the exact sülution fur ylz Xtzy

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Q: chuk thisynncdrs and gaph the if O-0,7 Curve r-4a Coso

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Q: Find the are length of the polav Curve r=3° from o-0 to 0= 1

A: Solve the following

Q: Find the length of the following two-dimensional curve. (21+1,3/24 r(t) = 2 3 for 0 sts6 L- (Type an…

A: To find The length of the given two dimensional curve.

Q: with Lagrange Inter lola tion » fmd the Pelynomie with minimum degree that involves the Points be Po…

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Q: Compute the length of the curve 3ti – 6tk over the interval 8 <ts 18.

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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: (6) Suppose the closed curve C in R? starts at the point (-1, 1), goes along the parabola y = r? to…

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Q: O Eind Hhe equatian af a, parab-alic the bist fit far Curve which s Hhe o given pictare. fallawing…

A: Consider the given data points. x y −3 7 −1 4 2 0 3 1 5 6

Q: Find the length of the curve. 30) x = 3 ty 3/2 - y 1/2 from x = 16 to x = 25

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Q: 12) Find the exact length of the curve [4,16] on 3

A: We can find the exact length of the curve as below,

Q: 1 5. Trace the curve r = 2 - sinocos³o.

A: Since, you have post multiple question. I am answering the first one. Please post the question with…

Q: The necessary and sufficient condition for a given curve to be a plane curve is that t = O at all…

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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: (b) Suppose C is a curve of length N, and ||F|| < M, where M is some positive number. Prove that F.…

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Q: If z = x + iy, then the inequality |z + il < 3 is a: A. Circle with center at (0,1) and radius 3. B.…

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Q: 3e) if c is any Simple Closed Curve, evaluate f dz, if ü7is out side (ii) 7 is in side

A: We will solve it by Cauchy Residue Theorem ∫f(z) dz = 2πi×R where R is the Residue of the…

Q: Find the length of the curve. Vzti + etj + e-tk, Osts 3

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Q: 7. Let fz) = z +1/z. Show that the level curve Imf(z) = 0 consists of the real axis (excluding z =…

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Q: Explain why a cubic Bézier curve is completely determined by x(0), x (0), х(1), and x'(1).

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Q: Let a cubic B-spline curve have knots 000 1 2 2 3 3 444. The domain knot values are between 0 and 4.…

A: The Solution is given below

Q: Let Cbe the curve given by: r(t) = 3costi – 3sintj + (3t + 1)k.0 stsnVZ. Then length of C is: 2n 12n…

A: Length of arc of curve = integration of mode of 1st derivative of function with respect to…

Q: nath A = 30, B = 20, C = 11, D = 22. 3. Discuss how to evaluate Z enclosing the origin. dz, where C…

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Q: 9) Sketch x = indieate the onientatiba of the 2t°, y = 3t, -4sts4 aud with %3D Curve an arow,

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Q: 4. Find the are length of the curve from y=1 to y-4

A: The given curve is x=18y4+14y-2 from y=1 to y=4

Q: 5 Find the valume of the Sotids abtaind by-revelving the Yegion in the firstquadrand boundby the…

A: Sketch the graph and find the region. Using shell method, volume is evaluated.

Q: (1) Give two different parameterizations for each of the following curves. (a) The line segment from…

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Q: A Bezier curve is defined by PO (0,0), PI (2,5), P2 (5,5) and P3 (7,0). Sub divide the curve at u…

A: We will get only one point as we have only one value of u. The given points are P00,0, P12,5, P25,5,…

Q: )مه و و ي (x2 + y?, y* + 4x) · dr (2,1) )هد0( )ه,(

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Q: the compler pleme Sketcl given by the Curve in Iz-31=12+3il %3D

A: Just use definition of modulus of a complex number.

Q: Every plane curve has a unique parameterization. O False. OTrue.

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Q: 1 y == (x² + 4)°%2 ,0 sxS 2 (x2 + 4)°/2 ,0<x< 2 6. deur die berekening van die volgende bej…

A: The given function y is - y = 16x2+432     ........(1)Formula for calcualting the lenght of a curve…

Q: IFind the exact length of the curve x= 3t -t, y=3t² ,0<t<2 ||

A: We have to find the exact length of the curve. The length of the curve is given by

Q: O A parhcle moves on a straight Iimes with velouty funchon V() = Sinwt uslwt f ind its position…

A: To find the position function from the given velocity function.

Q: Let C be the curve connecting (0,0) to (9,3) to (-3,3) to (0,0) using straight lines. Evaluate (sec…

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Q: 3) Find the exact length of the curve y = x² – In x for 1< x < 2. 1„2

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Q: apply stok's Theorem to evaluate (Ydz +7dy+ xdz) whereCiB the curve of intersection of x²+ y²+z² =…

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Q: Find the DE of the family of plane curves describe and sketch some of its members. Straight lines…

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Q: 5. Show that the following orthogonal families of curves: are x² + y² : = ax, x² + y? = by

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Q: Use Green's Theorem to find work done by F = 2°yi + (y – 3)3 along the curve c, C is the closed path…

A: We will find out the required solution.

Q: 1- Fit a least-square geometric curve y = ax to the following data 2 3 4 5 y 27.8 62.1 110 161

A: We have to find Geometric Curve using least square method.