Use Cauchy's integral formula to evaluate the following integral. z² J|2|=2 (z − 1)4 dz

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Q: What is the order of the symmetry group in R3 of an n-prism?

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A: We know that a number λ is called an eigenvalue of the matrix A if there is a non-zero vector x such…

Q: a)log5 1 20 b) log, 4+ logg 6

A: Log of the number

Q: B. Directions: Perform the indicated operations on functions. Given: f(x)=x²-10x +25, g(x) = x +5,…

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Q: 3. Consider the canonical basis {₁,2,3} of R³ and let F = {f₁, f2, fs} be defined by =(1,0,-1), 72…

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Q: Question 8 Obtain G.S. (xy + x) dx = (x²y² + x² + y² + 1) dy Moving to the next question prevents…

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Q: Show that every element of GF(pn) can be written in the form ap forsome unique a in GF( pn).

A: In this question, we have to show that, every element of GF(pn) can be written in the form ap for…

Q: Find the volume of the solid generated when the region enclosed by y = √√√x +3, y = √3x, and y = 0…

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Q: D = A= = Γ1 0 0 0 01 00 00 10 00 4 π 0 √2 23140 3 0 1 1 E = 27 0 5 0 0 0 √2 0 00 10 001 F = [100 0]…

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Q: 1. Suppose A is a 3x3 matrix. Suppose det A = 12 which are necessarily true ? a) AX-B has an…

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Q: Max Z = x₁ - 2x2 subject to: X1 + 2x₂ <= 7

A: We solve this LP using graphical method.

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Q: Consider the graph of the function f (x)=x²-x - 30. (a) Find the equation of the secant line joining…

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Q: Generate differential equation by elimination of arbitrary constants.

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Q: f(x) = 2x + 1; ¹/f = x² d.x

A: Solution: Given, f(x) = 2x + 1;  dfdx=x2 We have to check whether f(x) = 2x+1 is the solution to the…

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Q: pound semiannually  in what

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Q: Differential equations -Undetermined coefficients a) x + (3x + 1)y=e-3x dx dy b)x+y=e* b) x dx

A: A differential equation of the form y'+p(x)y=q(x) is called linear differential equation and…

Q: +∞ (-1)" n=1 3+1 Determine if the series Σ+ Use Alternating Series Test. is convergent or divergent.

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Q: Use the SQUEEZE THEOREM to evaluate lim x →+∞ 3 sech x+sin² x In x

A: Given,         limx→∞ 3sechx+sin2xlnx.

Q: With this function Plal-log, X. Use the properties of the reciprocal a function to trave a…

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Q: 1. Solve the given system of linear inequalities. 3x ≥ y 2x-2y24 x+2y ≤14

A: To solve the system of inequality  Consider the inequality and graph all of them in same graph…

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Q: List all the polynomials of degree 2 in Z2[x]. Which of these areequal as functions from Z2 to Z2?

A: We know that a polynomial of degree 2 has the representation fx=ax2+bx+c, where a, b and c are…

Q: If | a | = 2, then find the value of |à ×î ³² +|à × ³² +|à× ²².

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Q: Solve the following differential equations by separation of variables.  Show complete solutions

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Q: Third Derivative The third derivative of a function f(x) is the derivative of the second derivative…

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Q: j(x) = -3(x+1)³x² 2/x²³³+x+1)/x² 3

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Q: Find all complex solutions of the equation 8x4 -√√3-i = 0. Write the roots in exponential form and…

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Q: Problem 10.7_2 Find the Taylor expansion of f(z)=(z-1)e about the point z=1.

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Q: (5) Let A be an mxn matrix. The row space of A, denoted rowspace(A), is the span of the row vectors…

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Q: diagram

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Q: O Ln (x² + 1) 1|2 (y + 1) 2 + y 2 - y = C

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Q: Solve the given system of linear inequalities. 3x ≥ y 2x-2y24 x+2y ≤14 Solution:

A: A system of inequalities can be solved using graphically. Graph the system of inequations and the…

Q: Determine the truth value of (~pVg) → (q~r) if p and q and true statements and r and s are false…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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Q: arthmetiol function let alm) be an we define HR by Ace) - Za(m); 40x)=0 if x²1 nsx P cho dozirative

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Q: If {v1, v2, . . . , vn} spansa vector space V, prove that some subset of the v’s is a basis for V.

A: Let S=v1,v2,…,vn be a spanning subset of a vector space V. If S is linearly independent, then by the…

Q: y²dy = x(x dy − y dx)e>

A: We have to find the solution of the differential equation  y2dy=x(xdy-ydx)exy

Q: 4. Find all the element of Z/8 that have order 8. Find all the elements of Z/9 that have order 9.…

A: In this question,  we have to find all the elements of ℤ8 that have order 8, all the elements of ℤ9…