5. Triangle JKL with verfices J(1,-1). K(2, 3), and L(3, -2): x=4 J': L': K'

Q: A natural cubic spline S on (0,2] is defined by Jsin - 1+2-r. S) = if Osr<l. |S,0) = 2+ b - 1) + cư…

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Q: 3. Show that the line integral + 2xy) dx + x² dy + 2xz dz, is independent of path in R3, where C…

A: We will find out the required value.

Q: Evaluate the line integral S 3ydx + 6xdy where C is the straight line path from (1, 2) to (6, 5). So…

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Q: Suppose F(z, y) = zyi+ (# – y)j and C is the triangle from (4, 0) to (-4,0) to (0, 4) to (4,0). (a)…

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Q: Use Green's theorem to calculate §. -y² dx + xy dy where C is the vertex triangle (1,3), (4,0) and…

A: Consider the given integral. I=∮c-y2dx+xydy The green theorem is defined as, ∮cPdx+Qdy=∬R∂Q∂y−∂P∂x…

Q: 4. At the point (0, 0) the graph of y 4.x2 has greater curvature than does y 2x2.

A: These equation represents parabola,then Radius of curvature: K=  y'' /([1+(y')²]^3/2)

Q: 2. Find the coordinate of the points on the cardioid r=1- cose at which there is a horizontal…

A: We are given the polar curve: r = 1- cosθ use formula:         x=r cosθy=r sinθ then,  dxdθ=-sinθ+2…

Q: S find the Voutofeguatin 3x€-1rinthe interval Co,1] bg using:- - Bisectin method

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Q: 28. Evaluate by Green's theorem (x - cosh y) dx + (y + sinx) dy, where C is the rectangle with…

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Q: 3 K find OXA Curd A) at

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Q: Find the area of the inner loop of the curve r= 1-2cos θ

A: For the inner loop of the curve 1-2cos θ=0⇒2cos θ=1⇒cos θ=12⇒θ=cos-112⇒θ=π3,5π3

Q: Find the length of the curve. 33 x = 11t°, y =,, 0sts 3 33 t on 0stsv3 is The length of the curve x…

A: Ans: The length of the curve is 77

Q: The value of the line integral fydx + xydy over the straight-line path C from (0, 0) to (1, 2)…

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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: 1. A such that the difference in distances between (x, y) and two fixed points (called is the set of…

A: A___ is the set of points (x, y) in a plane such that the difference in distances between (x, y) and…

Q: Let C be the shortest path that connects t to ni and I = S. (coshz + 1)dz. Then I=0 1--sinh π+…

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Q: Let X,Y,T be dotined poinds. Show that if Te X Ÿ then XY = %3D

A: It is given that on considering that let X,Y,T be the distinct points The objective is to show that…

Q: Sketch the region enclosed by the given curves. y = tan(7x), y = 2 sin(7x), -77/21 sxs 7/21 y y 3 3…

A: For sketching the region y=tan7x, y=2sin7x, -π21≤x≤π21. Let y1(x)=tan7x, y2(x)=2sin7x, -π21≤x≤π21 We…

Q: Use Green Theorem to evaluate $ xydx+e'dy where C is the path from (0,0) to (1,1) along the graph of…

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Q: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

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Q: Compute the point of intersection of the curve sinx and x-1 with the help of Bisection method. Ans.…

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

Q: How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1…

A: Solution is given below:

Q: 1.13 Evaluate the line integral $ x*dx + xydx where C is the triangle with vertices at (0, 0), (0,…

A: The given function is x4dx+xydy By green's theorem, the integral becomes, ∫06∫06∂M∂y-∂N∂xdxdy where…

Q: Find the arclength of y = 2x /2 on 1 < ¤ < 3 2x3/2 uostion

A: given that y=2x3/2. we need to find the arc length in the interval [1,3] the arc length formulae is…

Q: 9. Evaluate the line integral / (2x – 3y) ds; where C is the line segment from (-1,0) to (0, 1)…

A: 9.

Q: 3 Find the Minimum distance from the origin to the plane X+2y-z=5

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Q: Show that the line integral 22 +2ry) dx + x? dy + 2xz dz, is independent of path in R, where C runs…

A: We will find out the required values.

Q: Compute ,f for f(2) +6 + 6i, positively oriented. sin(32) and path 2 that is the boundary of the…

A: Let's see the method of integration. We use residue method to solve this integral.

Q: How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1…

A: The given equation of the cylinder us x2+y2=1 in the half space y≥0. Calculate the value of ∫∫∫xzdV,…

Q: (4) Find the -periockic points and detorimme their sta. stakliny of hu)=EX %3D

A: 4) Given: h(x)=1-x3x+1 Determine the periodic point by substituting h(x)=x.…

Q: Suppose F(x, y) = xyi + (x - y)j and C is the triangle from (4, 0) to (-4,0) to (0, 4) to (4, 0).…

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Q: about the line x = -2 ソ=2× ソ=2° 1 2

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Q: Let C be the shortest path that connects 7 to ni and I = f. (coshz + 1)dz. Then --sinh π+ π(1- )…

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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: Evaluate the line integralf, (xy + z)ds along the line segment C from (1,2,3) to (-1,1,5).

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Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0), (2,2) and…

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Q: Evaluate the line integral x²z ds, where C is the line segment from (0,6, 2) to (8, 5, 1).

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Q: Use Green's Theorem to evaluate 5x*dx +xydy where C is the triangle with vertices (0,0), (1,0),…

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Q: Find a curve through the point (1, 9 whose length on the interval [1, 2] is given by i VI+ 25z!0dz-…

A: Explanation: Given a curve, ∫121+25x10dx Function f(x) has an arc length on the interval [a,b] is…

Q: Findd Fhie boundled by Ahe Cureo area 2. X= 3J-y' and x+Y=3 ーレ

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Q: 8. Use Green's Theorem to evaluate px*dx+xydy where C is the triangle with vertices (0,0), (1,0),…

A: As we know from the Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydA And The expression for the equation of…

Q: 2. Compute the line integral of E from B(0,0,0) to A(2,1,3) if E = -4xyax - (4y + 2x2)a, + 8zaz. Use…

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Q: use the funda men tal Theorem of Culculus to find the under Curue of 2. y = -xFl0 x between x = 3…

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Q: OFind the aquahon of the Hangent to the at point Lircle X2 +8Xt PCI,3)

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

Q: Evaluate the line integral 3xy ds where Cis line Segment Joining (-5,7) to (3,1) the

A: Introduction: A line integral in calculus is an integral where the function being integrated is…

Q: by thể differen ntial equation on associated with this sy

A: In this question, the concept of Laplace Transform is applied. Laplace Transform The Laplace…

Q: 1 Find the points have minimum distance From the origih to the Surface xyz =1.

A: Using the lagrangian ultiplies Let For critical points,

Q: 10. Find a tangent plane to z² – x² +y² = 1 at (7, –5, 5).

A: To find a tangent plane to the given curve at the point (7,-5,5)