sin TZ Let f (z) Find the residue of f (z) (z – 3)² at z = 3

Q: sin(t) ppose F(2) = ) dt. Use the Fundamental of Theorem of Calculus to calculate F' (1). 9+t (z) =

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Q: 8 sin x Find an antiderivative F(x) of the function f(x) such that F (0) = 1- 3 + cos r

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Q: sin TZ Let f (z) = Find the residue of f (z)at z = 3 (z – 3)2

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Q: 7. Evaluate using the residue theorem eir dx x2 +1

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Q: sin TZ Let f (z) = Find the residue of (z – 2)? f (z)at z = 2 -

A: We have to find the residue of f(z)  at z=2

Q: 9] Expression for R(x) in f(D)y = R(x) which is solvable by the method of %3D undetermined…

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Q: (sin2z, if 0<zs zz + b,if<zs1" Q4. Let g(x) Derive the values of a and b so that g is continues and…

A: Given, the function g(x)=sin2x,  if  0&lt;x≤π6ax+b,if π6&lt;x≤1. We have to find the value of a and…

Q: a. Let ƒ(x) be a function satisfying 0 ƒ(x) 0 … x2 for -1 … x … 1.Show that ƒ is differentiable at x…

A: The differentiability of the function can be determined with the help of the left-hand derivative…

Q: f(x) = [sin x if 0 T

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Q: sinz Calculate Rz-4|<T z(z-R)² dz using Residue Theorem. |z-4|<n z(z-n)²

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Q: (a) Use the Product Rule twice to prove that if f , g , and hare differentiable, then (fgh)'   =f'gh…

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Q: (a) (b) Find the residue of f(z) = sin at z = π. Find the residue of f(z) 2²-3z 2²+4 at z = 2i. =

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Q: 8 sin? a 00 i. x2 + 5 xp-

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Q: sin TZ Let f (2) = . Find the residue of f (z) at (z – 10)² - Z = 10.

A: We have to find the residue of the complex function fz=sinπzz-102 at z=10. Since we don't have…

Q: sin(x³ + y* ) Q3. Find of for the functions: .(x.y) (0,0) x'+y f(x.y) = .(x.y) = (0,0)

A: f(x,y)=sin(x3+y2)x2+y2 uv'=vu'-uv'v2

Q: a) f(x) = 1+ Sinx for all x e R

A: According to the question, we need to plot the graph of the function: f(x) = 1+sin x The graph of…

Q: Q2: Show that u = ln(x² + y2) is harmonic function and find the conjugate harmonic v = (x. y) and…

A: Given: u(x, y)=lnx2+y2 To show: u(x, y) is harmonic function and find its harmonic conjugate v(x, y)…

Q: 2-Consider the function defined by the base i) Find dz (ii) Prove that x дz ?x - дz ду z =…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: 3/2 Fir nd the arc length of the curve f(x) ==(x-4)°, 7<; -) Find f'(x) ) Express the arc length as…

A: See the details solution in below

Q: Let a > 1 be a constant and y = (9e- sin z 3) In(x+a). Find y'(0).

A: Product rule of differentiation:…

Q: -Consider the function defined by the base: Find dz ) Prove that дz +y əx дz ду = sin 2z z =…

A: Topic:- application of derivatives

Q: Z-T 4. Find all singularities in C for the function f (z) and their residues. sin? z

A: We can solve this question using definition of singularities and residues

Q: Fundamental Theorem: 2x sin t -dt. Find the value of f'(x). t2 +1 Let f(x) = | %3D

A: We can solve this as follows:

Q: dx -= In[F(x)]+C• What is F(/3) if C = 0? For J (x+x³) (x Tan-'x+1) + 6 + -1 +

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Q: Let a > 0 be real. Use residues to evaluate the princi- pal value of the integral R 1+ cos ax lim…

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Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f near…

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Q: the function f (2) = z Cos z ̟has a zero of order 1 None

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Q: (c) Let ɛ be a number so that 1 > e > 0. Explain why the integrals dx, dx x2 -1 can be computed…

A: For (c), Let ε be a number so that 1&gt;ε&gt;0. Now, we will show why ∫ε11x2dx,   ∫-1-ε1x2dx can be…

Q: a3z a3z 5. For z = x?siny show that дудхду ay²əx

A: As per our norms we have to write one question at a time kindly repost remaining questions.

Q: sin(t) (F(x³)). dx Suppose F(x) dt. Use the Fundamental of Theorem of OCalculus to calculate 6+t

A: SOLUTION-

Q: lim EV2x; + (x;)²Ax n→00 can be expressed as a definite integral on the interval [1, 8] of the form…

A: Given query is to convert limit into integral.

Q: n 1 ² Σ (sec (2 + ²) - 2 (2 + ² +)) - nxn i=1 3. Express lim as a definite integral, f(a)da.

A: This is a integration problem

Q: a) f(x) = 1+ Sinx b) f(x) = x² + 2x- 1 c) f(x) = 2* + 2 for all x eR for all x eR for all x eR

A: Given function are: [1] f(x) = 1 + Sinx   for all x ∈R [2] f(x) = x2 + 2x - 1  for all x ∈R [3] f(x)…

Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f near…

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Q: (등공) of and ôf Evaluate for f (x,y) = sin (3 x- 2y) at 36

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Q: III. Let f(x) = 2 sin x 1. Use the local linear approximation of f at x = 0 to approximate e2…

A: Given problem:-

Q: sin TZ Find the residue of f (z)at z= 6 (z – 6)² Let f (z)

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Q: lim x" sin is NOT zero when: x→+∞ O a 1 a > 1

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Q: Find all the singularities of tan(z) f(z) = determine their types, and compute the residues at the…

A: Given function is fz=tanzz. We have to find the singularity of fz. Now, limz→0fz=limz→0tanzz00…

Q: 21. Evaluate ſ dx by using Residue theorem. 2+x4

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Q: dy -x²()+5y= e3X +cos 2x is The ODE: X dx 3 dx Linear of order 4 Non-linear of order 3 Non-linear of…

A: If a differential equation when expressed in the form of a polynomial involves the derivatives and…

Q: 10. Prove that 7/2 75/2. sin 0 cos (cos a cosec 8) de 10 T 2 (1-cos a).

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Q: sin TZ Let f (z) = Find the (z – 10)² residue of f (2)at z = 10. -

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Q: sin TZ Let f (2) = Find the residue of f (z)at z = 3 (z – 3)?

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Q: Let F(z) = | sin(5t) dt. Find the MacLaurin polynomial of degree 7 for F(z). 0.69 | sin(5z*) dz. Use…

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Q: 1. Find the derivative using the Fundamental Theorem of Calculus, Part I, without evaluating the…

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Q: Consider the function. y = -7 sin-(x) (a) Decompose the function in the form y = f(u) and u = g(x).…

A: We have a function to find part (a) and (b).

Q: find Fourier sertes [0, 2w] an O f = X COS X

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: poles of f(z) = 1/sin(z) and determine their residues.

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