Find the series for cos⁡x/(1+sin⁡x ) by differentiating the power series of ln⁡(1+sin⁡x ). With sigma notation

Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

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Q: (3) Argue briefly that the following properties hold. (a) For any outcome s E S, we have Pr[s] < 1.

A: To show that for any outcome s∈S, we have Prs≤1 that is probability of any outcome is less or equal…

Q: 3n4. (-1) n° +1 Major Topic 3. (a) Analyze the convergence of n=1 (b) Analyze the convergence of…

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Q: Let A, B and C belong to M(3,R) such that: det(A) = 10, det(B)= 10/5 and det(C) = 3, then…

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Q: For the following differential equation y = x * (x + y) + 2 and the following initial condition y(7)…

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Q: g. Find all lower bounds of (48, 72}. h. Find the greatest lower bound of (48, 72}, if it exists.

A: Given Poset is ({2,6,8,12,18,36,48,60,96},|), where "|" denotes the "divides" relation.   (g) To…

Q: 5) B = [(1, 2, 0)T, (1, 1, 1)T, (1, 0, 0T)] is an ordered basis for 3. a) Find [v]B, the coordinates…

A: A change of basis consists of converting every assertion expressed in terms of coordinates relative…

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 5…

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Q: Write the equation in exponential form. Assume that all constants are positive and not equal to 1.…

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Q: 2. sVr .: s Vt

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Q: Secondary Topic 1. Let g(r) = 2" + 3". Find (g-1)'(5).

A: y=2ˣ+3ˣ y'=2ˣ ln(2)+3ˣ ln(3) (g⁻¹)'(x)=1/[2ˣ ln(2)+3ˣ ln(3)] (g⁻¹)'(5)=1/[2⁵ ln(2)+3⁵ ln(3)]…

Q: Prove: If x, y, z are integers with x2 + y? = z², then either x or y (or both) is even. Hint: Do a…

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Q: If m rst = 164, what is m<RVT?

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Q: 3) Solve the following IVP. y" 4y 3(4) (o if te3 gre)=?exr(ase) if tz3 where "exp(x)= e et

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Q: For the graph of y = f(x) shown to the right, find the absolute minimum and the absolute maximum…

A: The absolute maximum of a function on an interval is the greatest possible value where the function…

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: Evaluate the double integral to the given region R. xy" dA; R = {(x,y)| 6<xs 10, 0sy s 1} R , ху? dA…

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Q: LINEAR PROGRAMMING SIMPLEX METHOD 1. A Western shop wishes to purchase 300 felt and 200 straw cowboy…

A: According to the given question we need to maximize z=300x+200y                1 x= Felt hat…

Q: 2. Given the conditional statement, Construct a statement as to the following: "If the angles in a…

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Q: (1) 5z(x) – lo /b

A: Option that give equivalent to 1 are A F G

Q: sin(r2) – . (c) Find a power series for and write down the first three non-zero terms explicitly.

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Q: Find the product of the following matrices, if possible. 4 1 7 5 0 - 9 -2 - 3 6 - 7

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Q: wael manasra edited 8:06 PM sinh(3 In(a)) = %3D (A) – 1 6a - 3 1 (B) a³ – 4 - (C) 을 +교 (D) 을-삶 1 2a…

A: We want to find the value of sinh(3 ln(a))

Q: Write out the sample space and assume each outcome is equally likely. Then give the probability of…

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Q: 5. Compute the 1st and 2nd degree Taylor polynomials L(r, y) and Q(r, y) for f(r, y) = In(r² + y?)…

A: 5 Given function is fx,y=lnx2+y2. We have to find the 1st and 2nd degree Taylor polynomial Lx,y and…

Q: Question 4 Let P = 2ax + 5ay - 3az, Q = 3ax - 4ay, and R = ax + ay + az. For what values of k is |…

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Q: let A= and Describe the sed of all vectors b for which the equatiön AX=b is Consitent.

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Q: The derivative of f(x, y) = e* sin y in the direction of 0 is given by cos y-V3 sin y Du f(x, y) =…

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Q: 5 Let (sn) be a bounded sequence, and let k be a non number. onnegative real (a) Prove lim sup(ksn)…

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Q: (7) Three cards are drawn from a deck without replacement. What is the probability that they are not…

A: Please find the answer in next step

Q: Find the inverse of the given matrix.   A= -4 -3 1 -4

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Q: 6. Draw the Hasse Diagram for the poset: ({{1), {2}, {4}, {1, 2}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3},…

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Q: 22 +6 -9 -6 Find the slope. 3 3. 4. -1 3

A: We want to find slope of given graph.

Q: Consider the following integer programming problem: xi +3x2 + 2x3 max s.t. x1 + 2x2 < 5, 4.x1 – 5x2…

A: Given: Integer programming problem                  Max  x1+3x2+2x3s.t.    x1+2x2≤5…

Q: Major Topic 3. (a) Analyze the convergence of (-1)" n +1 n=1 (b) Analyze the convergence of (-3)"…

A: (a) The given alternating series can be represented as follows:

Q: erify that 2; is an eigenvalue of A and that x; is a corresponding eigenvector. 2 -3 1 -6 11 = 5, x1…

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Q: Let Mn.n(R) denote the vector space of n x n matrices with real entries. Let f : M2.2(R) → R be the…

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Q: The vector tell f (xxz) = (z=+,2oxy"6) igven. Calkulate, using the stores theorem, the surface…

A: Given that  Fx,y,z=z2−1, z+xy3,6 To evaluate the integral ∫∫S∇×FndS using the stokes theorem.

Q: 2. Draw three different graph that has a Euler Circuit. (minimum of 5 vertices)

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Q: sin x - x limg0

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Q: Convert 487 to base 5.

A: The quinary number system uses 5 as the base. Any number in the quinary system can be represented…

Q: 3. The point (3,8) is on the graph of f(x) = 2*. Determine the coordinates of the image of this…

A: Given f(x) = 2x  Thus, (x, f(x)) = (3, 23) = (3, 8)  g(x) = 0.5 f[2x-4] + 3

Q: Using production and geological​ data, the management of an oil company estimates that oil will be…

A: Area bounded by curve y=f(x) i.e. area under curve from x=a to x=b Area  =∫abfx dx

Q: Evaluate , (V. A) dV for the vector field A = x²yi +xz³j- y²z²kwithin the volume of a cube defined…

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Q: Find the radius of convergence of the power series. (If you need to use o or -oo, enter INFINITY or…

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Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: To find a parametric equation of the line tangent to the curve of intersection of the surfaces at…

Q: Consider a $250,000 home mortgage in which the payment per month is $1063.57 for a thirty-year…

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Q: Write an expression equal to - log, (c) · log (b) |using exactly one log. (hint: the base of the log…

A: Concept: Here we shall use the formula for change of base. logab=logcblogca Using the identity we…

Q: Secondary Topic 9. Use a third-degree Taylor polynomial to approximate e/2.

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Q: Let f(z) = ((z – 31) + 9)ez-. Evaluate fe f(2)dz, where C is Iz – 2i| = 2, positively directed. a) 0…

A: Given that fz=z−3i2+9e1z−3i. We have to evaluate ∫Cfzdz, where C is z−2i=2 positively directed. Use…