What additional information would you need to prove ATRO = AMT by the HL theorem? A TR TM R В ZOTM 2 ZTOR C TM OR OM = 2TO M

Q: Determine the area enclosed by the following curves r = 2 + cos 0 97/2 r = 4 + 3 sin 0 7/12 + v3/16

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Q: et zy = f sー n z = s %3D Ch) Find zqF zy White the sesubt on exact redangulet form,

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Q: (a) Consider the following line integral L(adar + ydy + (az – y)dz) along a curve C given by r =…

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Q: ECR 9s a sordon Area cvol CE) =V0ICE) ean Yntegraole on E Sand 主 After thet desariptron. 1ntegroble…

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Q: Wz bisects LXZY and X = LY. Which choice of method can be used to prove 4XWZ = AYWZ? O sS O AAA O…

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Q: Evaluate integral |C F*dr, where F(x,y)=xyi+x^2yj, and C is given by r(t)=ti+t^2j, 0<t<1 (< or =)

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Q: 2'ydy where 1/2 Evaluate the integral A) 64 z = sin(t), y = cos(t) %3D %3D D) 64 1/8

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Q: A muliple regresion of y on a cnstant x and x produces the folloing resuls. j= 4 +0.Ax + 0.9%, R =…

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Q: Evaluate the line integral J yds where C : r(t) = t²i + 2tj, 0st<3. Select one: O 3/10+ }(e – e-³)…

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Q: tind the value of the consrant (min) that makes the D-E j X dx -CyfmX) dy so (Homogeneous, exact,…

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Q: Evaluate (l. yz dV where E lies above the plane z = 0 and below the plane z = y, and inside the…

A: Given, ∫∫∫EyzdV, Where E lies above the plane z=0 and below the plane z=y and inside the cylinder…

Q: Complete the following proof. Given: XY 1YR, RS 1 YR XY Prove: SR YZ Y. R. RZ Because XY 1 YR, RS…

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Q: Čopy of Given the following noninoar ordinary difforantial oquation, y+5y+2y2=f (1)· where f(t) = 3…

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Q: ) USE THE METHOD OF VARIATON OF PARAMCTERS TO SULVE THE GIVEN ODE 8" +y'= secx Sec'x %3D

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Q: Comi der Hhe falßlning. J= x' J = 6-x of the ragan bj intyng awea ef mgount to O Fnd the wi th ayact…

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral (5 + Væ…

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Q: Suppose h(z) is analytic at z = 0 with h(0) = 4, h'(0) = i and h" (0) = 2 Compute the following…

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Q: consider Hthe quotien E ringzWI where I = (XtX+?) E Valuat e (zx+3+I)

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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: 1. Evaluate the integral: SSf, xe**+y<+zt dV where B is the portion of the unit ball x² + y² + z² <…

A: Here, the region B is the portion of the unit ball x2+y2+z2≤1 that lies in the first octant.…

Q: The value of the line integral | F(r).dr when C F(F) = [-y, -xy]and C is the upper half circle arc…

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Q: Use Green's Theorem to determine the value of the following line integral 1 I - (7 x + 3 y ) dx + (…

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Q: The value of the integral oIm(iz)dz, where C:| z|= 2, counterclockwise, is

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Q: Evaluate the integral ſc(x+y+ z)dr, where C is the helix parametrized by r(t) =, for 0 <t < 5.

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Q: The integral /4x? + 4y? + 42² dV тп, R where R is the solid hemisphere with x? + y? + z² 0 Find the…

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Q: W hich of the following is not a cylinder? Justify your answer. 4x² - z?= 1

A: Given that , the equation 4x2 - z2= 1 To determine given equations represent a cylinder.

Q: By making an appropriate change of variables, evaluate the double integral = || (x + y)e²-y° dædy R…

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Q: 12. Evaluate by using Stoke's Theorem [sin z de - cos x dy + sin y dz] where C is the boundary of…

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Q: Consider the following cylinder in R°. x² + z? = 49 a. Identify the coordinate axis to which the…

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Q: Evaluate the triple integral 2xe" sin z dV, where Q is the rectangle defined by Q = [(x, y, z)| 0…

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Q: Evaluate the integral. | (sec?(t) i + t(t2 + 1)3 j + t6 In(t) k) dt 34 i tan (t) + j 8. + k 4 49

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Q: 3. Evaluate the integral cosh ™z dz, z(z? + 1) Izl=2 where the circle |z| = 2 is described in the…

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Q: If the region R is bounded between two circles x² + y = 4, x² + y = 9, then we have: sin(Vx2 + y?)…

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Q: What is the value of the closed integral cos(Tz)/z with respect to z within the closed circle /zl =…

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Q: 15. Evaluate the contour integral e3z I (z+ 2)ªdz where C' is the circle |z| = . 9e6 2 O 27 9e-6 O…

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Q: ots) Evaluate the following contour integrals: Sc (z² – z + 2) dz, C is quarter circle connecting i…

A: Given  ∫(z2-z+2)dz, C is a quarter circle connecting i to 1C∮(z2+z)(z-3i)2, C:|z|=5C

Q: c). For each of the given paths, verify Green's Theorem by showing that [y³dx + xºdy=ff(xXx dA.…

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Q: What is the value of the double integral (y tar tan y-z+2) dA, where D= {(z,y) | z² + y² < 4}? %3D…

A: By finding the limit points of integral you can find the value of integral as follows

Q: 1) In rectangle JKLM, JN = x + 3 and JL = 3x + 1, select all that apply. %3D %D K N M A) NL = 4 B)…

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Q: Evaluate the following iterated integral. 1 16 12y dx dy ? 0 9 Vx+y2

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Q: By making an appropriate change of variables, evaluate the double integral (x + y)e²"-v° drdy where…

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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: Consider the following cylinder in R°. x² + z? = 25 a. Identify the coordinate axis to which the…

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Q: POSSI What additional information would you need to prove ATRO AOMT by the HL theorem? A ZOTM LTOR R…

A: HL theorem (Hypotension Leg theorem) states that two right triangles are congruent when their…

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