Re(z) dz, where C is the right half circle |2| = 3, from z 2² – 2i (Ъ) -3i to z = 3i.

Q: COSTZ (iii) dz, where C is the Jc (z²-1)2 circle |z – 2| = 2 counterclockwise.

A: Let fz=cosπzz2-12 and C is the circle z-2=2 fz can be written as fz=cosπzz2-12=cosπzz-12z+12…

Q: 12: A tangent to the circle x² + y? = 5 at the point (1,2) and th circle x? + y² – 8x + 6y + 20 - A)…

A: Given that  A tangent to the circe x^2+y^2=5 at the point (1, 2)

Q: 1 dz (z² + 9) Let Cb the circle |z - 3i| = 2. Then (6+ 32 2 πί TT 3 O none of these

A:

Q: 20. The tangent of the acute angle between the y= 4x-3 and y=x-5 is 2 (A) 5 [B) [C) 3 (DJ The radius…

A: tan(θ)=m1-m2/1+m1m2

Q: B. Evaluate sin z z²+j2z dz, C the boundary of the square with vertices ±1, tj clockwise.

A:

Q: Solve the problem in an unknown interval z E [0, a] using transversality condition J = min y(1),a.…

A: Solution:-

Q: Use the previous exercise to write the equation of the circle ofradius 5 and center (3, 4) in the…

A: Standard form of a equation of a circle whose center is (h, k) and radius is r is, x-h2+y-k2=r2

Q: jw F(w). [a - acos (wr)] - A 1 Tjw jwF(W) = -2A (1-cos (WT)). Tjw jwF(W) = -2A (asin ² (WT)) Tjw How…

A: since we have a trigonometric identity:                                   cos(2θ) =1-2 sin2(θ)⇒ 2…

Q: (c) Evaluate L A – 423 + 4z² dz where C is the circle |z – 2| = 1. , z4 – 4z3

A: Given,       ∮C4z+2z4-4z3+4z2dzwhere C is the circle z-2=1

Q: Use Green's Theorem to find SF ·dř where F = (y³, –x³) and C is the circle x² + y² = 3. %3D %3D

A: The given vector is  F = y3i - x3j

Q: Show that [(x- y) dx + (x – y)' dy] = 3ra" taken along the circle x +y =a° in C the counter…

A:

Q: 1) Evaluate F dr where F(r,y) = ri and C is the half of the circle %3D ²+y 3 16 lying below the…

A:

Q: cos TTZ 6. Evaluate -dz, where C is the circle |z| = 4 c 23-7z+6 ezt

A:

Q: Find Df and Duf to:- XZ on the point (,,1) inthe direction of V = 2i -3j+6 K. %3D soLiin ansi- lo

A: Directional derivative of the function.

Q: Set up and simplify (but do not evaluate) : 3x ds, where C is the arc of the circle r2 + y² = 4 from…

A:

Q: 35. In the xy-plane, the circles with equations (x-3)² +y² = 11. and (x+2)² + y² = r² |3D %3D 2re…

A:

Q: Evaluate where C is the portion of the circle centered at the origin with radius 2 in the 1st…

A:

Q: 32. (sin y, x) • dr, where C is the boundary of the triangle with vertices (0, 0), 0 ), and 2' 2

A:

Q: 6. Evaluate [(x + y²)dx – xdy where C is the circle "x²+y² : = 1" with a counter- clockwise…

A:

Q: Prove that the curve y:(-,) → R³ is regular with factor H and determine whether the image y (t) = (2…

A: To determine : the      included in a plane in   or not. Here,…

Q: 6. Let C C R? be the positively-oriented boundary of the graph of the circle x2 + y? = 1. Using…

A:

Q: Prove that the curve y: (-,-)→ R³ is regular with factor H and determine whether the image y (t) =…

A: If γ't not equal to 0 for all t∈-π2,π2then it is regular. If γ''t=kγ't for all t∈-π2,π2 then the…

Q: 4. Evaluate y ds where C is the upper half of circle x² + y² = 9, traversed in the counterclockwise…

A:

Q: What is the angle between the lines M ww x-2 y+4 z-3 x-2 y-5 1 2 E-3 and 1 1 O a. /2 arccos(/3) OC.…

A: Given two lines: x-21=y+42=z-31 and x-22=y-51=z-32

Q: (y - eCos(e25! dx + (x2 + y+1) dy, where C is the circle r = 2.

A:

Q: 2 Green's theorem, evaluate ((+) dx + 3xy dy where C is the circle * +y = 4.

A:

Q: tind the area of the parametric curve X = t ,4=9t-73

A:

Q: 2. Use Green's Theorem to evaluate (7z +y) dy - (r² – 2y) dz where C is are the two circles as shown…

A: theorem:

Q: /| 9(x + y) dA where R is the region that lies to the left of the y-axis between the circles x2 + y?…

A:

Q: VI 23) Consider the region in the second quadrant between the ciréies X²+y?=4ard x?7y==25 ?-25, and…

A:

Q: 3. Evaluate ff, (x² + y²)³/²dA, where D is the region in the first quadrant bounded by the x-axis,…

A: Given problem:- Evaluate ∫∫D (x² + y²)3/2 dA, where D is the region in the first quadrant bounded by…

Q: The circles r (V3/2, 7/3). Show that their tangents are perpendicular there. V3 cos 0 and r = sin 0…

A:

Q: ez 16. Evaluate dz, where: (4z-1) cos(Tz) a) I is the circle |z| = 1/8 traversed once…

A: We need to evaluate the complex integral in the following three regions represented by Γ,

Q: 29. Let C be the quarter of the unit circle in the first quadrant, traversed coun- terclockwise from…

A: Explained below

Q: (27=2 + 26xy + 10x – 2y°, 13x2 + 30y² + 2x³ + 22y)and let C be the circle a2 Let F = + y = 4…

A:

Q: 5. Evaluate (y +tan x)dx+(x -2ry+y)dy, where C is the circler +y' =4 and is oriented in a positive…

A:

Q: 2. Use Green's theorem to evaluate fe e-x³ dx + (5x + sin(y²)) dy, where C is the circle x² + y² = 4…

A: Please see the below picture for detailed solution.

Q: Evaluate fe(11 +x³)dx + 76dy where C is the line segment from (0, 1) to (-2, –1) followed by the…

A: We will first break the whole path into two segments and then integrate on both segments.

Q: (3²+ 3a)dA, where D is the region in the 3rd quadrant between the circles 2² + y² = 1 and x² + y² =…

A:

Q: (a) Evaluate sin 2z dz, 3z -71 where C is an anticlockwise unit circle centred at the origin. 4.

A:

Q: B. Evaluate sin z z²+j2z dz, C the boundary of the square with vertices +1, tj clockwise.

A: Evaluate the integral ∮Csin zz2+j 2z dz, where the path C represents the boundary of the square with…

Q: 2z-1 Find the upper bound of e 5z +4 where C is the right half of the circle z= R, R>2

A: Factorize the denominator of the function inside the integral z4+5z2+4 as z-2iz+2iz-iz+i. From this…

Q: 2e? Let f (z) = -Let C'be the circle z = 7in the counter-clockwise direction. (z – 3) (2 – 5) Part…

A:

Q: b) Find the points on the curve 2 17x + 12xy + 8y“ = 100| that are farthest away from the origin…

A: Substitute x = rcosθ and y= rsinθ

Q: 2. Find the value of the integral 3z3 + 2 Je (z – 1)(2² + 9)dž, - 1)(2² + 9)' taken counterclockwise…

A: The solution is given as

Q: Find an upper bound of the absolute value oI e +1 (a) dz, where C is the right half circle |z| = 3,…

A: Note:  Since you have posted multiple questions, which are independent, as per our policy we are…

Q: Integrate counterclockwise dz by Cauchy's formula 9. - 3 counterclockwise around the circle C : |z –…

A: Given that integrate counterclockwise  ∮Cz2z2-9dz by Cauchy's formula where  C : |z-3-3i|=32π.…

Q: 8. centered at Which of the following equations represents the circle with radius F 16x2 + 16y2- 16x…

A:

Q: Q4: Evaluate fo z² - 3z + 1 z + 2i -dz 312 where C is the circle |z + 11 = ²/

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.