ii) You invest $10000 in a mutual fund which grows at a certain percent every year. After 8 years your investment is worth $16000. At what annual rate is your investment growing?

Q: . Compute the central difference approximations of O (h^4) for the first derivative of y = cos(x) +…

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Q: 17: Which of the following directions is descent direction for f(x) = 2x1 + x² - 2x₁x₂ + 4 where Xo…

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Q: Q₁. A: Find x²dx by using Riemann integral. √x=0 Q, B: Let f' be a continuous function on [a, b].…

A: Lets solve both questions

Q: -1 3 -6 -4 -3 4 Let y = ,Vi= " 5 -1 Compute the distance d from y to the subspace of R4 spanned by…

A: The distance of a vector from a subspace can be evaluated using the norm. For this, we have to find…

Q: Find the solution of the Euler equation on (0, ∞) with initial conditions x²y'' + xy' + y = 0, y(1)…

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Q: Given the following matrices. Solve for the following: 15 25 58 81 2 14 A= 10 11 5 B = 42 3 -1 -6 42…

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Q: -31 B -9 .The QR factorization of -6 [/²/3 - 1/√√/2] 3√√2 = ] 0 2 - 1/2 √2) (a) Applying the QR…

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Q: Q: Find A least-sayvares solutions of Ax=b 1 -2 3 - 1 2 O d 3 ", 5 : دا 1 -4

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Q: The intensity of light I (measured in luxes (lx)) at depth y (in m) below the surface of a lake can…

A: You post more than three subparts questions, as per our guideline we can solve only first three…

Q: F2016 The polynomial f(x)= ar +7x²-9x+b is divisible by 2x-1. The remainder when f(x) is divided by…

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Q: O Consider the following matrices 0 ^- (-¹2 ~) -- († ;) -- (1 ¹/² : ;) -- (:) --( : ) 1/2 3 A = D= 1…

A: We will use property of matrix multiplication  Two matrix can be multiplied only when number of…

Q: Provide an example of a topological space that is connected but not path-connected,why?

A: We use definition of connected and path connected sets. We use contradiction method.

Q: Z is a complex number

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Q: Taylor Series Approximation Formula f" f"" (a) ² f(x) = f(a) + f'(a)(x − a) + ¹¹¹(a) (x − a)² +…

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Q: Assume that f(x) ~ Σ an sin(nx) on [0, π]. What is the Fourier sine series of f(2x) on [0,7]?

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Q: mperature T of a heated circular plate with the origin being at the ce 64 T(x,y) = x² + y² + 2 point…

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Q: If u and v are the two solutions of d'y dy dx² + P + Qy = 0 dx uv₂u₂v + P (uv₁ - u₁v) = 0 (uv₁u₁v) =…

A: The given differential equation is d2ydx2+Pdydx+Qy=0.....(1) To prove: (a) uv2-u2v+Puv1-u1v=0…

Q: * 2: The function f(x) = x² + 2x² + 3x² + 4x₁x₂ + 5x₂x3 + 6x1x3 can be written in the form f(X) =…

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Q: Use the Laplace transform to solve the initial value problem where y'' - 3y' + 2y = f(t), y(0) = 0,…

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Q: Consider the function f(x) = 1 + 2x + 3x² + 4x³. Let s be the sum of all distinct real roots of f(x)…

A: First derivative check for monotonicity

Q: Suppose that Y₁(t), Y₂(t), and Y₂(t) are solutions of the differential equation y"+5y"+(2-t)y=0.…

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Q: A(t) = 3t²i - (t+4)j + (t²-2t)k B(t) = sin(t) i + 3e-¹j - 3cos(t)k Find d² (A x B) at t=0 dt²

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Q: C e

A: Given: Graph with 6 vertices To find: Euler's trail or explain why the graph does not have an Euler…

Q: 1 ++²)

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Q: Create a proof for the following argument 1. P v (Q⊃R)   2. (S v L) ⊃(Q * X)   3. Q ⊃~P   4. S…

A: We prove the given argument by using rules of inference.

Q: Find the Fourier series of the function f(x) = |x| which is defined over the range - TT<x< TT.

A: Fourier series of the function

Q: 2 The function f(x) = ax³ + 4x² + bx-2, where a and b are constants, is such that 2x - 1 is a…

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Q: The standard form for (F.O.D.E) y = 3y' - 4x + 5 is 4 5 y'-y = 3x 3 Option 1 4 5 y' - 6y=3x-3 Option…

A: Firstly we make the coefficient of y' is 1 and convert into the standard form  y′+p(x)y=q(x)

Q: Evaluate the integral by completing the square and using trigonometric substitution. dx s √5 + x −…

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Q: ulsu (un (a) u

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Q: 06) Find the Area bounded by the curves y = √√x and x = 2y - y² ,with sketch.

A: To find the area bounded by the given curves :-

Q: Given that f(x) = x³ – 0.3x² − 8.56x +8.448. - Use polynomial interpolation to compute f'(x) and…

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Q: Hand written plz 2. Standardize the following LP model. - max z = −3x₁ + 8x₂ − x3 + 12x, - 3x₁ +8x₂…

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Q: -3 -2 -1 x(t) + 0 -1 3 t

A: The given problem is to find the Fourier coefficients and Fourier series expansion for the given…

Q: Express the region as a union of Type I or Type II regions and evaluate the integral ffy dx dy. YA 1…

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Q: o q Lor -00 10 The function determining the shapes above is f(x) = a√z. The area shown on the first…

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Q: Question 2. Let E be the solid region inside the surface x² + y² + z² = 25 and above the surface z =…

A: Given, surface x2+y2+z2=25and anothersurface z=3x2+3y2 E be solid region inside surface x2+y2+z2=25…

Q: The given matrix is an augmented matrix. Write the corresponding set of linear equations for the…

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Q: 3x + 2y = 4 2x − y =-9 x + 3y = 13

A: We have: 3x+2y=42x-y=-9x+3y=13 This can be written as: 322-113xy=4-913 The augmented matrix is…

Q: 7: The point X = [0 0] for the function f(x) = 2x2 + x + 2 represents a A: Saddle Point for f(x) B:…

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Q: Investor Dan has $119,000 to invest in bonds. Bond A yields an average of 9.4% and the bond B yields…

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Q: Q4. Differentiate term by term the power series E-o(x-7)". dy Q5. Solve: = y² (1+x²), y(0) = 1. dx

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Hand written plz 2. Standardize the following LP model. max z = −3x₁ + 8x₂ − x3 + 12x4 - - - 3x₁…

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Q: Recall that the Fourier series of a function defined on an interval of te form [-L, L] is of the…

A: Since you post more than three subparts questions as per our guideline we can solve only first three…

Q: 8. Let f(x, y) be a cost function with two parameters: x and y, and f(x, y) = y³x²y² + y + 3. For…

A: Given the function  fx,y=y3-x2y2+y+3and xold=1, yold=0, ε=0.01

Q: The bacteria in a culture double every day. Which function can be used to find the number of…

A: In daily life, recurrence relation has wide application. Suppose an initial condition is given.…

Q: List all the subfields of the field F262144 in which the polynomial x³ + x² + 1 has a root.

A: (Subfield Criterion) Let Fq be the finite field with q = pn elements. Then every subfield of Fq has…

Q: (i) Use the chain rule to show that -3x = (In 3)32 dx Hint: use the fact that 3 = eln 3ª (ii) Use…

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Q: decimal places.) Show ALL work. 2³ sin(x)dx, n = 8

A: Given,            ∫04x3sin(x)dx;    n=8

Q: Which of the following gives the Golden ratio? X x+y where xy X c. YX+Y where xy x X [^\!** d. X

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