Estimate approximate derivative of f(x) = x2 at x = 1, for h = 0.2, 0.2, 0.05, 0.01 using first order forward difference formula

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A: Instantaneous rate of change is the slope of the given data . So, basically we have to find the…

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A: Given: Singular Valued Composition To find: Solution

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Q: Find the directions in which the function f(x,y) = x²y + e* sin(y) Increase and decrease most…

A: We have to find  the directions in which the function increases and decreases most rapidly at…

Q: with 5 and 8 the Di

A: a) As per logic,  5, 8, 13, 12, 7, 10, 8, 9, 17, 17, 16, 15, 13, 10, 5, 6, 11, 8, 10, 9, 10, 10, 2,…

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Q: (a) Use sigma notation to write the Maclaurin series for cosлx. (b) Use sigma notation to write the…

A: Polar coordinates can be represented by (r, theta) Where.     -π<theta≤π Or…

Q: Q2. Solve the following differential equation by variation of parameters: d²y x3 dx² +6x³. dy dx -3x…

A: Sol

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A: To find- If radius of convergence for power series ∑n=1∞anx - 3n is 2, then the series ∑n=0∞an.…

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Q: is poured into the tank a te of 2 liters/min. Let y(t ial model for (t) and gol

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Q: This exercise comes from Stein & Shakarchi, ch 2 # 6. Let be an open subset of C, and let TC be a…

A: We use Cauchy-Gaoursat Theorem.

Q: rection: Illustrate the need for an axiomatic structure of a mathematical system in Geometry by…

A: Given a figure and some statements. To provide a conclusion for each statement. The given figure is

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Q: 7. Find the eigenvalues and eigenvectors the system X' = [₁ 30. Use the eigenvalues and eigenvectors…

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Q: 2. Consider the following IVP y" + 5y +6y=0, y(0) = 2, y'(0) = 3. (a) Write the ODE as a system of…

A: Given: y" + 5y' + 6y = 0  To find: Solution

Q: (a) (i) For the finite arithmetic sequence 5, 8, 11,..., 44. write down the first term a, the…

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Q: 1) a) Evaluate the limit. 1 1 lim 3 x x+3 x-3

A: Introduction: The limit of a function is the base of differential calculus. When the independent…

Q: Find the general solution of the DE

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Q: (a) (i) For the finite arithmetic sequence 5, 8, 11,..., 44. write down the first term a, the…

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

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Q: For the figure below find: $5x² + (2x + y)²dy (1,1) (1,0)

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Q: Write Fourier series for the function y=4n-k T≥X≥0

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Q: 2. For the quadratic function y = -6x² + (K + 4)x +9, find the following: a. The Axis of Symmetry of…

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Q: (7) The set H={0,1,2}is a subring of (Z4, +4,.4) integer ring module 4. T OF

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Q: (6)lf K is a simple ring, then K is a Jacobsen radical ring. T O F

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Q: Let F(x, y, z)= -2y71+ 2x j. Use Stokes' Theorem to find 7-d7, where Cis a circle parallel to the…

A: here we have to use normal for Stoke's theorem.

Q: The Laplace inverse of 5/(s^4) is: O Non of These O 5^3 Ot*4/5 O 415 51^3/6

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Q: Express e² in the form a + ib. (Simplify your answer completely.) z = 8- -22

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Q: T Q2/ Reversing the order of integration fxsinydydx.

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Q: Let f(t) be a function on [0, ∞o). The Laplace transform of f is the function F defined by the…

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Q: Q4. Solve the following by using Laplace Transform (i) sin 2te-t + 3 t5 - cosh t 2 t (ii) sin +…

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Q: Find the directions in which the function f(x,y) = x²y + e* sin(y) Increase and decrease most…

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Q: 3 Z Find the residue of z² - 1 2 Z at z→ ∞00.

A: Use the formula of residue at infinity to solve this problem as in next.

Q: Let T: R² → R² be the counterclockwise rotation through the angle Then the standard matrix of T is:…

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Q: (a) (i) For the finite arithmetic sequence 5, 8, 11,..., 44. write down the first term a, the…

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

Q: We consider the following differential equations: xy" + xy' - (x − 3) y = 1 pour x > 0. Give the…

A: Consider the following differential equations: xy''+xy'-(x-3)y=1 for x>0   To Find: General form…

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A: LPP of given problem is given by Maximize  Z = 90x1 + 110x2 Subject to constraints 2x1 + 4x2 ≤…

Q: Q6/(A)Evalute ſ² ſ₂ ex² dxdy. (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial…

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Q: (a) Show that the limit does not exist by considering the limits as (x,y) →(0,0) along the…

A: Let us find the limits of the functions in the next steps.

Q: Find the directions in which the function f(x,y) = x²y + e* sin(y) Increase and decrease most…

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Q: Find the optimal solution to the following problem. Minimize f (x1, X2, X3) = x₁² + 2x₂² + 10x3²…

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Q: Q.4) (a) Scratch the function X ㅠ - X (0 < x < π). Is it a periodic function? If so what is the…

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Q: CONSIDER THE FOLLOWING THREE TYPES OF VECTOR SPACES: (a) M2x2 (b) R³ (c) P3

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Q: Let g C[0, 1] be a fixed function. Consider the operator A = B(C[0, 1]) defined by (Au) (s) :=…

A: Compact Operator: A compact operator is a linear operator A:X→Y where X, Y are normed vector spaces…