(iv) Find [z dz along the contour C given in Figure. 1+i

Q: 4. Find the moving trihedral of the curve f(t) at the indicated value: †(t) = cos? t î + sin² t ĵ…

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Q: Let I = f x*cos(x) dx. The approximation of I using the two-point Gaussian quadrature formula is:

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Q: B) Use Green's Theorem to evaluate F dr, where C is the triangle with vertices (0,0) (3,0) and (3,…

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Q: 7. Find the length along the parametric curve defined by v(t) = (t, In(cos(t))) from t = 0 andt=.…

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Q: The tangent line to the graph of y = In(2x) is perpendicular to z + 4y = 1 at the point where Select…

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y², (12,…

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Q: (B) The length of the curve r(t)=(1+1)i+(1-1j+r/2k from the point t=- to the point r= is 2. -IN

A: The length of the curve means the arc of the length of the curve . The arc of the length of a curve…

Q: (a) R (T) = A cos @o T (b) R (T) = A sin on t (c) A - A (/to) which is a rectangular function of t…

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Q: D A Find thepolar eavation for the cartesian curve (x²ty) - A)r-4 cos o =4x. Br°=4 cos e c)r?=4cos o…

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Q: Consider the curve C shown in the figure, parameterized by: C: r(t) = (1 - cos(t), 1- sin(t), 1 +…

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Q: Find the equation for the tangent plane to the surface at the indicated point. (Hint: Solve for z in…

A: Let's find.

Q: Compute sin z dz , where a is the piece of the parabola with equation y= a?, which lies between the…

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Q: 4. Let C be the unit circle in the xy-plane, and S be the boundary of the square with side 1,…

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Q: Given the path C that is the line segment from (-4; 0) to the origin, and the curve y = 2x² from the…

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Q: Find the lengths of the curves r(t) = (2 cos t)i + (2 sin t)j + t2k, 0 ≤ t ≤ π>4

A: Given r(t)=2costi+2sintj+2tk We need to find the length of the curvature . The length of the curve…

Q: IV Evaluate f F. dR given that AF (1, y) = 2y i+ (ry – 2r)j and C is the curve in the third quadrant…

A: Hiii

Q: 6. Let f(r, y, z) = e=² cosh y + z ar ff at the point P in the direction of :

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Q: Determine the length of the curve 7(t) = (3t, sin t, cos t) on the interval 0 < t < 2n. %3D А. L =…

A: As we know that, The expression for the length of the vector-valued curve is: L=∫abx't2+y't2+z't2dt…

Q: Q1- The divergence of the function f= (r cos 0)e, in spherical coordinates is..........

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Q: 1. Evaluate z dz, where the contour C goes from z = 0 to z = 1 to z = 1+i.

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Q: The Normal to the curve 2x2 – y? = 1 at the point (1,1) is: %3D 3 y =-*+ y =x+ y = 2x + 1 %3D P. y =…

A: To find The equation of normal to the curve 2x^2-y^2=1 at the point (1,1)

Q: What are the principal parts ant all the poles of f=1(e^(z) -1) ?

A: Given

Q: Find the length of the curve r(t) = (cos 3t, sin 3t, 2t3/2),0 sts 3. %3D

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Q: Find the length of the curve. r(t) : cos(8t) i + sin(8t)j + 8 In(cos(t)) k, 0 stS T/4

A: Solution is given as below:

Q: 12. Evaluate 3x ds where C is the parabolic are along y from P(0,0) to Q(2, 2).

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Q: 1/B) Find the length of the cardioid 'curve: r = 1 + cose

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Q: nd the points on the given curve where the t r = 1 + cos(0), 050 < 2n prizontal tangent r, 0) = %3D…

A: Given curve is  r=1+cosθwhere 0≤θ≤2π.

Q: Given F(x, y) = [arcot(/K)-(secx)* - 2y]i+ 3x-es 2021 evy and the curve C=C,UC,UC, as shown in the…

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Q: Find an equation of the plane tangent to the following surface at the given point. V3 A,1, sin (xyz)…

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Q: Find the equation for the Tangent Plane on the given surface coS ax – x²y + e*z+ yz = 4 Po(0, 1, 2)

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Q: 1. Sketch each curve in the z-plane, and sketch its image under w = 2². (a) |z1|=1 (b) x = 1 (e) y²…

A: We are authorized to answer three subparts at a time since you have not mentioned which part you are…

Q: where C is the curve r(t) = (sin(t), cos(t), sin(2t)), 0 ≤ t ≤ 2

A: Given C is the curve                        r(t)=sin(t), cos(t), sin(2t), 0≤t≤2π and…

Q: The length of the curve r(t)= [cos(t), sin(t), – 3t]with 0 <t<2n is equal to O A. 2/5 T O B. 2/6 T O…

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Q: The divergence and curl of the function f(r,6, 4) = (r* sec 0)e, is .....

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Q: Draw direction field of the DEQ below, by hand, and sketch an approximate solution curve that passes…

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Q: 1. Sketch in the xy - plane the domain of each function : (a) ƒ (x, y) = (Vx – 1+ Vy +1) · In (x² +…

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Q: Find the length of the curve. r(t) = cos(4t) i + sin(4t)j + 4 In(cos(t)) k, 0 <t< t/4

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Q: Find the Length L of the curve R(t)= -2cos(4t)i + 2sin(4t) j + t k over the interval [2,6]. L =

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Q: Let C be any curve.

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Q: - Find the aera under the curve y = cosx Form x = 0 to x = -fx sec² (ax² )dx a#0

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Q: Find the length of the curve. r(t) = cos(3t) i + sin(3t)j + 3 In(cos(t)) k, 0 <t< n/4 %3D

A: Find the length of the curve:…

Q: The parametric form of the tangent line to the image of f(f) = (4i², 2,t – 3) at t = 2 is L(t) =

A: To find the parametric form of the tangent line to the image of f(t)

Q: The parametric form of the tangent line to the image of f(t) = (3t2,,t – 2) at t = 2 is L(t) =

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Q: 3.8 If H = (x – y)a, + (x² + zy)a, + 5yz a, evaluate f H dl along the contour of Figure 3.28.

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Q: ind the equation of the plane in the figure, which is tangent to the graph f(x, y) = 0.2x + 1.4y –…

A: Equation of tangent plane to the surface x=f(x,y) at point (a,b) is…

Q: Use Green's theorem to find the k number that satisfies (k + 3) ∫C((k/2)*(x^k)*(y^2))dx + ((yx^(k +…

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Q: The tangent line to the graph of y = In(2x) is perpendicular to a + 4y = 1 at the point where Select…

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Q: Consider F and C below. F(x, y) = 6xy? i + 6x²y j (re), e + cos{ nt), Gnt)), osts1 C: r(t) = (t +…

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