Exercise 15. Let f(z) cos z (z2-1)2 The residue off(z) at zo = 1 is a) – sin 1 b) sin1cos 1 c) -(sin 1 + cos 1) cos 1 d) O a. O b. c. d.

Q: Find the four values of t between -2π and 2π at whichsin t = cos t

A: Our Aim is to find the four values of t between -2π and 2π at which sin (t)= cos (t)

Q: 2. If z = cos 0 + i sin 0 where 0 is real, show that 1 1 - i tan- = - 1+z 2z 1-z2 Express: а) 1+z2…

A:

Q: Find the maximum and minimum valucs of f(x) = sin x + cos x on (0, 2n].

A: Given function:                      f(x) = sin x + cos x,   x∈[0, 2π] Use the second derivative…

Q: 2. By hand, sketch the following against independent variable t: a) x₁(t) = Re(2e(-1+j2m)t) b) x₂(t)…

A:

Q: 3i +2V2 - 5n -4i +6(1 +a T/4 [(3sec2 t)i - (5 + sin t)j - (6sec t tan t)k)]dt Find 0. 2 2-57T-4 3i +…

A: ∫sex2xdx =tanx+c∫(constant)dx=x+c∫sint dt =-cost +c∫sect tant dt =sect+c tanπ4=1cosπ4=12secπ4=2

Q: Find the form for a particular solution to the equation y "+2y'– 3y =r?cos (nt). A…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Let r(t) = (sin(t), cos(t), 2 sin(t) + 9 cos(2t)). Find the projection of r(t) onto the xz-plane for…

A:

Q: Use the residue Theorem to show that T Cosh 7 2 sinh 7' 2 sinh² 7. 22 -1 -dz 3Di Se (22 + n²)² sin z…

A:

Q: El cálculo de la integral, S sin' (z) dz es equivalente a Seleccione una: O a. - sin (2a)+ S [1+ cos…

A:

Q: Use the Residue Theorem to show that sin²x ㅠ f² = 0 x2 dx = FIN 2

A:

Q: Let r(t) = (sin(t), cos(t), 6 sin(t) + 9 cos(2t)). Find the projection of r(t) onto the xz-plane…

A: Given vector…

Q: Exercise A3.5. Show that sin(z) = 0 if and only if z and that all the zeroes of sin are simple. (The…

A:

Q: 1] Evaluate (a) -S (s²+1) ² {t sin (b) S 1/2 5² (s² +¹)² (d) S

A: Find Laplace of tsin(t/2)

Q: (b) Using the Fourier integral formula , show that cos Tw -sin xwdw = {2 if 0n

A:

Q: x-1 c) Let f (x) = x+ 0. Find by using numerical calculations in a tabular x2 - 1 which x approached…

A:

Q: Show that cos jx is orthogonal to cos kx in C [ -π,π] for j ≠k,j,   k >=1

A: As per the question, we have to prove that two specific functions are orthogonal in the Hilbert…

Q: Determine the pole ac the residue at A(z) = Ite² and ach pole Sinz +ZcOSZ

A: Step 1: Step 2: Step 3: Step 4:

Q: |(4e + 3z² – 3 sin z)dz =. O 4e² +z – 3 cos z + c O 4e² +z³ – 3 sin z +e O 4ez + 13 + 3 cos z + c O…

A: integration

Q: Cos z Residue of cos. at z = 0 is %3D 1. 1 -1 3. 2 4. 0 2.

A: The residue of a function: f(z) at z=a is defined as Resz=af(z)=limz→az-af(z).

Q: Use the residue Theorem to show that -1 T Cosh T 生 2 sinh T Je (22 + 7²)² sin z 2 sinh around the…

A:

Q: |(4e* + 4x – 6 sin æ)dx O 4e* + æ4 – 6 cos x + c O 4e* – x4 + 6 cos x + c 4e" + x* – 6 sin ¤ + c O…

A: We have to find the integration of given function

Q: (a/3 d(cosx) =? 24 - sinx O A) V3/2 O B) 1/2 C) -1/2 O D) -1/3 E) T/3

A:

Q: (D² – 2D- 3)y = 2sin x a. y, = -cosx – 2 sinx =csx COSX b. y, = --cosx - - sinx COSX c. Y; = - cosx…

A:

Q: A particle moves so that r(t) = (3 cos t + 3t sin t)i + (3 sint – 3t cos t)j+ (2t² )k. Find the…

A:

Q: e) Find all solutions of 1+ cos? x = 2cos² [0, 2.7). in the interval 5e.

A:

Q: cos z = cos x cosh y– jsin x sinh y

A: Complex numbers

Q: A graph of f (z) =a cos(br) is shown, where b is a positive constant. |(0, 4) (T, 4) |(27, 4) -2…

A:

Q: The f sec$30 sin 30 d0 is {A} sec*30 + C 12 {C}-cos*30 + C {D}cos 30 + C 12 {B} sec 30 + C 18 18

A:

Q: Evaluate L. (4² COST (x² + a²)² da, where a > 0, using the residue theorem.

A:

Q: 1) Solve det [i4(îĥ.ở)] where ở li ). and în = COS + sin j. (i = V-1)

A:

Q: Compute the derivatives of the given functions. d. a) dt d [5 sin ¹5t = FI

A: As per the Bartleby guidelines, answering only first question as the other questions are not the sub…

Q: Evaluate f 2ema cos (nx) dx 2ema [n cos (nx) a. m2+n? m sin (nx)] + C b. 2emz [m cos (пa) n sin…

A:

Q: Classify the zeroes (according to order) and isolated singularities of (2² - 1)e¹/² cos (TZ) (z + 2)…

A: