4) Exercie S Hst 2x+iy be a complex mumber such thet (-s(37)#0Then Re (tent3z))|c equal to: Sin Bx co$3 nb (Bx) cosh (3x) $in(3x) cos3x dost(30)+sin Rt (35) Nune bf these.

Q: Suppose f(x) = sin 4-x). Evaluate: x) dx (A - 3cos FC B -cos 3 X-4+ C 3 Cos 3 (D) 3cos -x- 4)+C

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Q: FCx): 2x-5xナ3 find f'co).

A: We are solving the first question and for the next question post the question again and also mention…

Q: Show that there exists a complex number z such that z" +cos(| z |):(1+31z*)=0

A: The complete solutions are given below

Q: Let F = (3z + 3x²) i + (6y + 4z + 4 sin(y²))j + (3x + 4y +6e²² (a) Find curl F. curl F - (b) What…

A: We will use result of part c  which gives line integral in closed curve and combined it with line…

Q: cos 2x he ƒ -dx is 4+sin 2x {A} In|4 + sin 2x| + C {B} In|4 + sin 2x| + C {C}(4+sin 2x)² + C {D} -(4…

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Q: Q1/: a: Using the relation showthat Jv2 (x) =, cos x

A: See the attachment

Q: √4x+4-√√5x+1 x#3 Q18) if f(x)= x-3 k x=3 A) 15) 1 C)O by Q19) Use local linear approximation in ind…

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Q: 921) Which of the following is an odd function A) cos xsin x 11 sec.x C). DUNK DOOV

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Q: 3) Show that the function 13-212+2 g(2) = is a Complex differontiable function ait the point 20 =1…

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Q: Q3 Find and show the work for (x+3)(3x+2) dx. (a) х (b) F (sin(2x) – cos x) dx. (c) S(3x² + 2x +…

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Q: sin (2x) dx (x²+L)(x-3) 3) (sin (2x) 88

A: We solve by Contour integration.

Q: Part (b) 5e Evaluate -dz by residue theorem, where C is the contour |z| = 2 6z4 +30z3

A:

Q: Determine if the setsin² {sin²x, 1-cos(2x)} is linearly dependent or linearly independent on I =…

A: Let B={sin2x,1-cos(2x)}.

Q: b)- dx a(13-x)(2+hncr)) + Ja9 differentiating on both sides dy (13-2) (2+dnc) da b9 de + be9) %3D de…

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Q: )L{sinh(7t) + (2t + 1)U (t – 1)},

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Q: Q17) The slope of the tangent line of the curve x² + y²=5 at the point (1,-2)- A) √√4x-4-√√5x-1 x-3…

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Q: a) _*? (1-x²)Z x+3 b) S- x2+2x+5 c) Find the value of sin(tan-1- sec-d) dx d) S x² Vx2+1 e) S Vx2+2x…

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Q: Question 2 * SE sec2 (0) d0 = dx a) sec² (x³) - 3x² b) – sec² (x³) · 3x? | O ) sec² (x³ ) d) – sec²…

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Q: In integrating the function f(3x + 5)(cos) dv using integration by parts, what would you choose for…

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Q: Đi bỏ xes xdx = dx 2) √ √9+4x² = a) 6e5-1 25 ¹ (²3) + a) cosh-1 c b) 1+4e5 25 b) (4e5-1) 25 c). sinh…

A: Using following formulas

Q: Q3) A: Find y if: a- y = sin 2x + 2 cos x c- y = sin √x (As... b- y = secx. csc x d- y = tan(2x + 1)

A: Please see the attachment

Q: Evaluate _i(z³+i³) 2 z +1

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Q: Let f(z) : D C be a complex function. Is it possible for both f(2) and f(z) to be analytic? 2. • If…

A: Solution

Q: Fra) = Sin (2t) Find the 7h taylor Polynomial of

A: Given function is  Fx=∫1xsin2tdt

Q: Is sin(z) bounded in the complex plane?

A: In mathematics, a function is said to be bounded if there exists a real number M such that the…

Q: 1. Differentiate. a) f(x) = x43x b) g(x) = x² — e√x -

A: We need to perform differentiation.

Q: Determine two funetions f and g whose produet result in (f x g)(=) – 8 sin"I+ 27.

A: see below the answer no need of explanation

Q: The antiderivative of the function sin (Gx+7) is:

A: Given : sin12x+7

Q: 6) Use Linear Property to find ( 1- 3 x4)' A) (1- 3 x4) %3D B) – 4x3 C) - 2 D) - 12 x3 7) Use…

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Q: Q) prove that (1) -2P xSinx 2.

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

Q: Calculate the imaginary part of  ∮C(Re(z)+3.78)(2z^2+ 5z+ 13 / z)dz  where C:|z|=1  Use FOUR…

A: We have to find the imaginary part of the integral ∮ fzdz, where fz=Rez+3.782z2+5z+13z over the…

Q: f(2) =2x² + y+i(y² – x)

A:

Q: cosh (z) = eIz-e-iz 2i +e-iz 2i +e- 2 2

A: Use the standard formula of hyperbolic cosine function.