ulus I Spring20 dy let y = ztan then is rod dz 00 Select one: cot z a zlan + sec z ln z ) tan z b. lanz + sec a In r cos z Clan + sec? z lu z tan z d. ztan + sec z In z ).
Q: d sec (z) = dz sec(z) tan(z) sec? (z) o tan(z) tan (z)
A: We can find the derivative of the function by following the rules of differentiation and this…
Q: Evaluate the line integral C ydx + zdy - 2xdz; where C is the helix r(t) = costi+ sin tj+tk , 0 <= t…
A: To evaluate the given line integral.
Q: (a) Let f(2) = (z +4-i) (z+ + 5z³) Using CRT, evaluate the integral f(z (2)dz, where the contour Cis…
A: According to our company policy, we are supposed to answer only one question at a time. For the rest…
Q: Find div F and curl F if F(r, y, z) = 2e""i – 9 cos yj+ 4 sin? z k. div F= curl F
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Q: Find S, F· dř tor F = -5yỉ + 4x} – 4zk if C is the helix x = cos t, y = sin t, z = t, for 0 < t <…
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Q: Find the area outside "r^2=9cos(2theta)" and inside "r=2-cos(theta)"
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Q: Let f(r, y, 2) = e tan(r*z²). Compute fry: (r, y, z) . Simplify your final answer. %3D
A: We will find out the required value.
Q: Let Yzo.r parametrise a circle with centre zo and radius r (positive orientation). Evaluate the…
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Q: Soru 5) y' – y²secx + y tanx – cosx = 0 Riccati diferensiyel denkleminin bir özel çözümünün y1 =…
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Q: Q, Determine the PDF for multiple RV Y (a) Y, = X,tXz+ X3 Con dition Xi,Xz, X3 are wni formly…
A: Let us consider Irwin-Hall distribution as follows: Let X1, X2, ...., Xn be a random sample of size…
Q: 2. Evaluate fs ryzdS, where S is the cone with parametric equations r = ucos(v), y = usin(v), z = u,…
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Q: dy let y = (sin z) m = then is %3D da Select one: 1. a. (sin æ)™- tan r In ¤ + –In(sin z) b. (sin…
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Q: Curve C is oriented Counter owoy Arom the pozitive 오-axis 2- y, y? 21 %3D intersection af their surf…
A: Given, w=dx+x+ydy+x2+xy+y2dz. It can be written as, w=1,x+y, x2+xy+y2.dx,dy,dz It is known that…
Q: O show mat me Nomal point @ X= a( Coro +o Smo) y= a(8in0-o Cor0) dy Sine %3D ep" of Normal S-ゴ」=…
A: the parametric function is x=a(cosθ+θsinθ) y=asinθ-θcosθ Differentiate each with respect to theta…
Q: Find div F and curl F if F(x, y, z) = 3e*"i – cos yj+ 7sin? z k. %3D div F= curl F=
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Q: Find div F and curl F if F(x, y, z) = 7e*i – 6 cos yj+ 6 sin? z k. div F= curl F=
A: DivF and curl F are evaluated.
Q: (oet ber the following model Y: X, B + X. B, + € Where aue mathices vec tors and B; aNe vectos K; x…
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Q: Let F(x, y) 4y i + (2x + ev)3. Calculate fe F · d7, where C is the circle of radius 2 centered at…
A: Given: F→x,y=4yi→+2x+ey2j→ To Find: ∫CF→·dr→, where C is the circle of radius 2 centered at 0,0…
Q: Find div F and curl F if F(x, y, z) = 10e*Y i – 6 cos yj+ 2 sin? z z k. div F= curl F=
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Q: a para on to express the area The portion of the plane y + 2z = 2 inside th Let u =r and v = 0 and…
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Q: sen z dz 31. tag z da = sen a dz = cos a - In Jcos z + C = In jsec z + C cos z 32. tag 2z dz = tag…
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Q: 37. ( sen z + cos z cos z | (tag z + 1) dz = In sec x + z + C %3D (sen y dy cos' y 38. tag y sec y…
A: We know that , sen (y) / cos (y ) = tag y And 1 / cos ( y ) = sec ( y )
Q: . 10 pts possible Which integral represents the arc length of e astroid shown in 27 1. I = 9 cos t…
A: Using formula of arc length.
Q: sin z dz (z²–1) 2 where c = |Z – 1| =; valuate at oriented lockwise? (12 M)
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Q: Evaluate the given contour integral, where C is unit circle z=1. 3e cosz 2z +4 -57 + 2z- 4i 3 z' +…
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Q: Find div F and curl F if F(c, y, z) = 9e®Y i – 8 cos yj+ 4 sin? z k. div F= 9 y eY + 8 sin(y)+4…
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Q: Inz Vz Inz-z dz 2. Je cos 3r dz 13. S- ze-lal dz 74: cscz cot z dz dr dz dr 3/2 dz 26. J. v9-2 6.…
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Q: find ow/ar if w = (x + y + z)², ar www w x = r – s, y = cos(r + s), z = sin(r + s) at the point (r,…
A: See the attachment
Q: Find div F and curl F if F (x, y, z) = 10e*V i – cos yj+ 3 sin zk. %3D div F= curl F=
A: div F=∂Fx∂x+∂Fy∂y+∂Fz∂z∂Fx∂x =ddx(10exy)=10y exy∂Fy∂y =ddy(-cos y)=sin y∂Fz∂z=ddz(3 sin2z)=3(2sinz…
Q: Find div F and curl F if F(x, y, z) = 9e"Y i – 2 cos yj+ 7 sin? z k. div F= curl F=
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Q: 10. Ray OQ bisects ZNOP. Calculate the measure of NQ if PQ = 24. %3D P NQ = 10 NQ = 48 %3D NQ = 24…
A: In △POQ and △NOQ ∠P = ∠N = 90° ( given ) OQ = OQ ( Common) ∠NOQ = ∠POQ (OQ Is angle bisector) △ POQ…
Q: (b) f(u) = tan(arccos u). FRAS SER UNIVE ERS %3D ERSI TY OF fficial que s test question question ion
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Q: ubegral Fa dx un ntegral as the areg of Q Assuming r>o,compute the tems ing the of r by interpret…
A: The given integrand indicates the circle: x2+y2=r2, with a radius of r units. Limit of the integral…
Q: Find div F and curl F if F(x,y, z) = 9e*Y i – 8 cos yj+ 4 sin? z k. %3D div F= curl F=
A: F(x,y,z)=9e^(xy)i-8cosyj+4sin^2zk ∇F=∂F(x,y,z)∂xi+∂F(x,y,z)∂yj+∂F(x,y,z)∂zk…
Q: 8. Set S be the bondary of the cube with side length 1 in Oc tant 1. Is in 6 pieces) Use Stokes…
A: (1) Over the surface ABCD ∫sx dy dz +z dz dx=∫01dz∫01xdy…
Q: Let T(r,s,t) = (r cos(s) sin(t), r sin(s) sin(t), r cos(t)) Find the Jacobian of T at (3, π/4, π/3)
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Q: Let F = 2y ln zi+ 2x ln zj + 2k. Which of the following(s) is/are applicable to solve F. dr where C…
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Q: Find div F and curl F if F(x, y, z) = 10e"Y i – cos yj+ 8 sin? z k. div F= curl F=
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Q: Evaluate the integral [yda+zdy – rdz along the helix C given by - X = = cos πt, y = sin ít, z = t…
A: Line integration of the vector valued fumction
Q: Calculate the curvature function for r(t) = (4 cos(3t), 7t,4 sin(3t)). (Express numbers in exact…
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Q: Find da of z tany-y cot z = 1. cot z + zec'y = IP O tan y -v c z dy tan y +v ae z O dz cot z- zsec y…
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Q: Find div F and curl F if F(x, y, z) = 7e*Y i – 6 cos yj+ 10 sin? z k. - div F= curl F=
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Q: S Which of the following integrals is the result of using Stokes' Theorem to find F.dr where F = and…
A: The solution is given below :
Q: O Identify all the ponts Crit) on Z=F(xcy)=cos (x+y) ot which tangent vecfors to Z=F(xcy) are…
A: Tangent vectors are parallel to x axis and y axis, so the tangent plane is parallel to xy-plane. So…
Q: 1. Isosceles Triangle XYZ with XY = ZY %3D 2. Line XY perpendicular to segment AB, where B lies on…
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Q: Evaluate CF · dr. F(x, y, z) = xi + yj + zk C: r(t)= 9 cos(t)i + 9 sin(t)j + tk, 0 ≤ t ≤ 2?
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Q: Use Green’s Theorem to evaluate ∮C squre toot of (1 + x^2)dx + 14x dy, where C is the triangle from…
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Q: A uniform and stationary magnetic field Ris perpendicular to the plane containing a circular…
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Q: In this exercise we show that the unit cylinder r²+y² = 1 can be covered by a single patch. Let U =…
A: PART A To show : x2+y2=1 x2+y2=ur2+vr2=u2+v2r2=r2r2=1 Hence, proved.
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- Which lines or line segments or rays must be drawn or constructed in a triangle to locate its a orthocenter? b centroid?A triangle is bounded by the lines y = x, y = -x, and y = 1 When setting up an intergral to find mass or inertia or whatever, why can I not set it up as integral(1, -1) integral(1, x) dydx and instead need to set it up as integral(1, 0) integral(y, -y) dxdyShow that the intrinsic equations of a helix on a cone of revolution are : K= 1/as and torsion=1/bs where a,b are constant step by step with all det
- Let S be the portion of the cylinder y = 1 − x2 with x≥0; y≥0, bounded by the planes z = 2, and z = 10 . If I=(image 1) then it can be stated that:Suppose that a thin metal plate of area A and constant density doccupies a region R in the xy-plane, and let My be the plate’s momentabout the y-axis. Show that the plate’s moment about the linex = b is My - bδA if the plate lies to the right of the line, andSuppose f(x,y,z)=1/(sqrt(x^2+y^2+z^2)) and W is the bottom half of a sphere of radius 6. Enter ρ as rho, ϕ as phi, and θ as theta. What are the integrated integral and limits of integration using spherical coordinates?
- If the path defined by z(x) from points C to W were rotated about the x-axis, what would be the volume of the corresponding solid of revolution created? Be sure to show all work.Find the volume of the solid S under z = 3 + 2 cos x^2 and restrictedby a triangle in the xy-plane with the vertices (0, 0),(6, 0) and (6, 2).This means we can use the Divergence Theorem to find the flux Let S be the surface of the portion of the solid cylinder of radius 3 centered along the z-axis that lies betweenthe planes z = 0 and z = 4. Find the flux of ~F = x~i + y ~j + z ~k through S, where S is given the outward orientation.
- A region R consists of a square bounded by the lines x = −7, x = 7, y = 0, and y = −14and a half disk bounded by the semicircle y = (49-x^2)^(1/2) and the line y = 0.Find the center of gravity, (x, y), of R.Let S be the portion of the cylinder y = ln x in the first octant whose projection parallel to the y-axis onto the xz-plane is the rectangle Rxz: 1 ≤ x ≤ e, 0 ≤ z ≤ 1. Let n be the unit vector normal to S that points away from the xz-plane. Find the flux of F = 2yj + zk through S in the direction of n.