A.W:-Evalwte the intagral Ic2 - i) dz where c is; line OThe straight 9= 2x jeining Aceso) to BC1,) A Co,0) to B (1,2i) The paralola y - 2* joining A Co,0) t. B(1,2;)

Q: MT NOTES ASK YOUR TEACHER In this problem, x = c, cost + c, sin t is a two-parameter family of…

A:

Q: The complex function fla)=ulx.y) + ¿elx.y) Con be differentiated ony point Tin complex opoce The…

A:

Q: a) Use polar coordinate to evaluate I √x² + y² dA R where R is the region bounded by the circle z² +…

A:

Q: Evaluate (z* + 1)dx around the circle [z]=1 A) 0 B) 2in C2 Evaluate fx8 (2x - 1)dx A) 1 B) 0 C) -1…

A:

Q: Use Green's theorem to find the k number that satisfies (k + 3) |a*y² d + (yxk+1 + y²) dy = 7680,…

A:

Q: A. Homo ge neous Higher Ordered DE (0-704 - 310° ° + 103o² 1030² + 1500 - 216) y:0

A:

Q: Consider The falloming Parumetric eguatin O54=?4V X Ct) Zsinct) +cos (t) Wing calulus , fund all the…

A:

Q: Q3: The value of the complex integral f, dz, where C is a circle [a] = 2 in the positive direction…

A: ### Q3: Value of the complex integralTo solve the integral∫C​z3dzwhere  C  is the circle  |z| = 2…

Q: Let = (0,0), and a = (2,-1) be points in R². Set G=B¹2 (0,1)={v = (x, y) = R²: d₂(0,v) <1} H = B¹¹…

A: Let, and  be points in  SetTo find:Sketch  and The coordinates system,, and  be points in  Set

Q: cot z dz

A: Cauchy goursat theorem: If a function f is analytic at all points in D and on a simple closed…

Q: do 10 please

A:

Q: 9. If ABC is an acute angled triangle then the minimum value of sin A + (1 -sin A)* + sin B + (1-…

A: Claim: for 0≤x≤1, f(x) = x⁴+(1-x)⁴ is minimum when x = 1/2  Proof: f(x) = x⁴+(1-x)⁴  So, f'(x) = 4x³…

Q: a) Use Green's theorem to compute f F dr where c is a circle of radius R oriented CCW and F(x, y) =…

A: Green's theorem:∫C[Pdx+Qdy]=∫∫T∂Q∂x-∂P∂ydxdy where T is the region bounded by a simple closed curve…

Q: y U(a, b) V(?, ?) h =b units T(0, 0) a units W(c, 0)

A: HL congruence postulate: According to this congruence postulate, two right triangles are congruent…

Q: The equation z? = 10 – x² – y? defines a/an %3D a) ellipsoid c) paraboloid b) cone d) hyperboloid

A:

Q: 18. What is the rectangular equation of the curve whose parametric equations are x = 2t, y= 2+ 3t*?…

A:

Q: 2. Consider the line r(t) = (4t+1,3, 2 - t) and the ellipsoid + + z? = 1. What is the distance from…

A: Consider the line  and the ellipsoid To find  distance from the point (-3,3,3) on the line to the…

Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

A: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is Then x…

Q: tind Yaduis ot curuature of the Curue O r= 2t i t (1+); - 2t k at (2,1,-2) 13 Brofi+tietk at the…

A:

Q: b) Find the angle between the surfaces x² + y² + ² = 19 and 2 = 2 x² + y²-7 at the point (3, 1, 3):

A:

Q: a Find the distance from the point pC,,1) to the plane 2K -3y+77=1

A:

Q: 1) Let z be a complex mumba and be any function. f c isa closed contour then f RIZ)dz is Im (812))…

A:

Q: In ARST, SV bisects y ZRST. Find the coordinates of point T in terms of a. S (a, a) 2a T?, ?) V (2,…

A: Given that, Let ∠TSV=θ and ∠VSR=θ(∵SV is angle bisector)

Q: drawn from the point A(2,10) on the parabola y = x^2 + bx + c Since the tangent is parallel to y =…

A:

Q: Let f (z) = 3O = 0 A = 10and B= 10 + 10iet C1 be the contour composed of the line segments OAand…

A: Solution  Given  A=10   ,  B=10+10i

Q: Corsider the curve given by C = CqU Cz U Cg Ine value of (1. 1) C: y- 32 A) 15 24 B) 72 C) 15 11 D)…

A: We have to evaluate the integral ∫Cxdx+x2dy Now we have three curves.  Now, C=C1∪C2∪C3, therefore,…

Q: 9/ Find the Vale of the integrel ) Losz+Retz)r Imtz)} dz 3 is the Straitht line Segment from Zero to…

A:

Q: 3. Use Green's Theorem to show that to where C is the unit circle x² + y² = 1 in the…

A:

Q: Evaluate [[[ =*dxcydz over the sphere x +y² +=² =1.

A: to find:- to evaluate the given integral.