1. 2. Calculate $1 tanz dzfor C:2-3= 1 C22-9 Calculate $ 2 + 322-5 dz when...
2. Consider the linear system -2.c + 3y + 2 = 5 4.c +9y-322 = 5 -2.c + 18y - 292 = 20 (a) Write down the augmented matrix of the linear system. (b) Find the reduced row-echelon form of your matrix from part (a). (c) Using your answer to part (b), write down the solution to the linear system. Clearly indicate which variable(s) (if any) you are using as a free variable(s).
(1 point) Evaluate the integral. Loretiste 23+2 dz (1 + 7)(3+5) Answer: (1 point) The form of the partial fraction decomposition of a rational function is given below. (3,2 + 4.1 +43) (1 + 4)(72 +9) А T +4 Br +C 1? +9 A= 3 B= 0 C= 4 Now evaluate the indefinite integral. si (3:2 + 4x + 43) dr = 3/(x+4)+4/(x^2+9) (1 + 4)(x2 +9)
1 5. Let A = dz, (2 – 1)2(2 + 2i)3 where I is the circle [2] = 3 traversed once counterclockwise. The following is an outline of the proof that A = 0, justify each statement. Jo Tz – 1)*(x + 2133 (a) For R > 3 show that A = A(R) where A(R) Som 1 (z – 1)2(x + 2i)3 dz, and I'R is the circle (2|| = R traversed once counterclockwise. 21R (b) For R > 3...
Let C be the curve (x - 3)2 + 9(y – 1)2 = 36, x +2y + z = 4, oriented counterclockwise when viewed from high on the z-axis. Let F be as shown below. Evaluate $.F. F.dr. F= (32² + 3y² + sin x? )i + (6xy + 3z)j + (x2 + 2yz)k $. F. dr= (Type an exact answer.) с
5. Compute the integrals 23 dz e2 22-9)' where C is the (positively oriented) circle with equation |z|-1. Justify
5. Compute the integrals 23 dz e2 22-9)' where C is the (positively oriented) circle with equation |z|-1. Justify
1 Evaluate ; dz,Cistheellipse + y2 = 1 c 2:+7:+3
2 +1 (b) Evaluate the contour integral dz, 22 – 9 where I is the boundary of the square D = {z E C:-4 < Re(z) < 4, -4 < Im(z) < 4} traversed once counterclockwise.
get the value of the following integrals
where c is the circle (abs)z=3
2 dz e*"dz , donde C (z+, uientes: A) φ
2 dz e*"dz , donde C (z+, uientes: A) φ
Find the shape of the quadratic surface. (1) a2-5y2 + 7y - 322 5 (2) 3x2 + y2 +622 11 (3) a + 4y2 - 2:26 (4) 2 +4y-3z 5
Va2 y da dy The region A is bounded by the curve: 2+y=Va 3. Evaluate C 2102 dz dy dz 4. Evaluate The solid V bounded by surfaces: z = 1-2, z = y , y = 0
Va2 y da dy The region A is bounded by the curve: 2+y=Va 3. Evaluate C 2102 dz dy dz 4. Evaluate The solid V bounded by surfaces: z = 1-2, z = y , y = 0