Evaluate following integrals. dx a) (x² + 1)(x² + 2x + 2)

Q: Solve, for z, the equation Inz = 4 - 3i.

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Q: y" +y' – 2y = 4e* – 2x

A: We have the given differential equation is y''+y'-2y=4e-x-2x2     …..(1) The auxiliary equation for…

Q: olx 3(2-3x)"

A: The objective is to solve the integral ∫132-3x4dx

Q: sin(3z) Let f(z) = and C: ]z – a| = 1. Then ſ. ƒ(z)dz = z2(z-n) а. 0 b. 2ni с. — 2пі d. None of the…

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Q: Exercise 8. let C be any closed simple curve and f(z)=lz+il. Then the integral of f(2) over C is 0.…

A: Given C, any closed curve.  And f(z)=|z+ i|

Q: (c) Show that (d/dz)z does not exist anywhere,

A: See the attachment

Q: Which identity of the following is true for the relation between the trigonometric and the…

A: By using the different relations between trigonometric and hyperbolic complex functions we can check…

Q: 2. Write each of the following numbers in the form of a + bi a) cos(3 – i) b) 2i sin h (4 – ni)

A: The given expressions are: a) cos3-i b) 2isinh4-πi Write each of the following numbers in the form…

Q: EXERCISES 1.1 Answers to selected odd-numbered problems begin on page ANS-2. 1. Evaluate the…

A: Since you have posted multiple questions with multiparts. As per guidelines we"ll solve only first…

Q: Applying auxiliary equation to find the general solution. y "– 7 y"-18y = 0

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Q: (A) h(x,y)= sinh r cos y+ icosh r sin y. O (B) h(r,y) = e" cos y + ie" sin y. O (C) h(r,y) = cos ry…

A: A function f is harmonic if ∂2f∂x2+∂2f∂y2=0

Q: Let z be a complex number. Then cos(3z)-i is unbounded in C. * False O True

A: From Liovilles thm we can say Every non constant entire function is unbounded.

Q: Q5: (a). Show that if h: IR2 IR and f= 2h3 + ih is an entire function, then h is a constant

A: An entire function satisfies cauchy reimann equation

Q: If Im{f'(x)} = 6x(2y-1) and f(0) = 3– 2i, f(1) = 6 - 5i. Find f(1+i). O (A) f(1+ i) = -6- 3i. O (B)…

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Q: Let z be a non-zero complex number. Then Log(z²) = 2Logz O if -T/2<Arg(z)<0 O if OsArg(z)sTI None of…

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Q: A quick approximation is sometimes useful when an exact answer is not required. (a) Given any…

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Q: (x+h)? – 2(x+h) – 3-(x²-2x-3). lim 2. Use the limit definition to evaluate

A: Given that limh→0 x+h2-2x+h-3-x2-2x-3h. Compute the limit as follows.

Q: Let (N, F, P) be a probability space. If E1, E2, ..., En € F 3. ( are events, show that for all…

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Q: © Applyjing guaphicd amlyin to silve the fallomng graphical analyin to selve the n pieblen. muximiz…

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Q: Let z be a complex number. Then coth(z+JTi) is equal to -tanhz O None of these tanhz cothz -cothz

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Q: he table shows both the number of a certain type of graphing calculator in demand and the number…

A: (a) Suppose the logistic function for demand is: Dp=a1+betp. Here, 60≤p≤210. Paste the values in…

Q: Write the first and second partial derivatives. g(r, t) = t In r + 13rt7 - 4(9) - tr gr = 9rr = 9rt…

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Q: 8) Find an upper bound on the integral where I is |z| = 2 CCW fra dz

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Q: 8 8 xdx (x² + 1)(x² + 2x + 2) 1 π-5

A: ∫-∞∞xx2+1x2+2x+2dx=-π5

Q: Find a Mobius transformation M that maps each of the following regions onto the unit disk D(0, 1).…

A: We will use the following property of conformal transformation : For the conformal transform : w =…

Q: Suppose that v1, V2, . . . , Vn are linearly independent column vectors in F“:* and let e1, e2,...,…

A: Given that v1,v2,…,vn are linearly independent column vectors in Fn,1 and e1,e2,…,en be the…

Q: Suppose the weight of pieces of passenger luggage for domestic airline flights follows a normal…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

Q: et f (1) = e², f' (1) = 5e², g(1) = –3, and g' (1) = 1. Find h' (1), where %3D h (x) = 9 (x) arctan…

A: We have to solve the given problem.

Q: A demand function and a supply function for the same commodity is given. D(p) = 35 -7 In p million…

A: a) 60 (Ps, S(PJ)) = (3,3.790) • Producers are willing to supply [3.790 millionunits at Below a…

Q: Let a be a complex number 0. What is the absolute value of a/ā? O (A) 1. (B) 2. (C) 3. 4. O 000

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Q: Given u=y3 – 3x²y is harmonic, find harmonic conjugate v - 3.xy² +x³ +c - 3.xy? +x? +c - 3xy? –x3 +c…

A: See solution below. We used property of CR equation and total derivative.

Q: True-False. If the assertion is true, quote a relevant theorem or reason, or give a proof; if false,…

A: (a) Consider the function fz=1sin1z. Observe that for any k∈ℤ\0, 1kπ is singularity of fz=1sin1z.…

Q: Suppose v1, V2, ..., Vm E V. Prove that {vı, V2, ..., Um}+ = (span(v1, v2,….., Vm))“.

A: Given,v1,v2....vm∈V To prove :      v1,v2....vm⊥=span(v1,v2....vm)⊥⇒v1,v2....vm  is a set of…