State the rules for approximating the definite integral  integral a to bwith the Midpoint Rule, the Trapezoidal Rule, andSimpson’s Rule. Which would you expect to give the bestestimate? How do you approximate the error for each rule?

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Q: If w= In(42) cos(2yz - 3), x = log(t), y = 4e²² and 2 = sin(t²-1). Find de

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Q: The converse of a statement of the form “If A then B” is the statement “If B then A .”  (a) Write…

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Q: 11. Consider the following function f: R+ → R+ meaning where the domain and range are both the set…

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Q: 6. SET-UP the double integral which gives the vol- ume of the solid in the first octant enclosed by…

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Q: State whether each of the following random variables is discrete or continuous 1. The number of…

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Q: 24. If P(An) ≥ e > 0, for all large n, then P (An i.o.) ≥ €.

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Q: Describe a technique for solving a set of data's numerical derivative. Include the nature of hae…

A: There are several techniques that can be used to numerically compute the derivative of a set of…

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Q: Find the general solution of the given system 6 0 0 1 X 1 0 0 X': =|1 1

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Q: Consider the matrices A = 1 1 [f] U = g h O V = 1 b b X 0 dB = 0 [f a 1 d g 1 C h 0 and X = y. If…

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Q: d-d Answer: d-(bvd) Kon

A: Since you have posted a question with multiple sub parts, we willprovide the solution only to the…

Q: (22) Let A = (-∞, -2] and B = (102, ∞). (a) Find an explicit bijection f: A→ (-∞, 0]. Justify your…

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Q: The Laplace transform of the function f(t)= -4e-3t+5f4 is Select one: True False L {f(t)} =…

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Q: Show that any sequence of positive real numbers either has a subsequence that converges, or else a…

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Q: Exercise 1.1.1 Show that the set of all continuous solutions of the differ- ential equation u"(x) +…

A: Answer given below.

Q: Given the vectors (1 10), (0 2 3), (1 2 3) in R3. Given vectors are linearly independent. Select…

A: We will solve both questions .  Questions are related to vector space . Let's solve

Q: Please do fast

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Q: Problem 4. Conduct linearization of the system near its stationary points and determine their…

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Q: Determine whether the following equality is true or false. 3 ff f(x,y)dA = [³ f√√¹8-x²ƒ(x,y) dydx D…

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Q: Copy of Evaluate: [2] = [√5] = [-3] = [-2.1] = For Blank 4

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Q: The set of degree 2 polynomials at²+bt+c, where c is even ; is a subspace of P2. a. True b. False c.…

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Q: ad q (> 0) the first of n harmonic m ers. Then prove that ((n+1)²) (n-

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Q: en 2 Given the region D enclosed by y² = x² and x² + (y+6)² = 18. Sketch the region D. Set up the…

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Q: Question 1 [ variables Given the function of two f(x,y) = −4x² − 6xy-7y²-1. a) Use Lagrange…

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Q: Use the convolution theorem to write a formula for the solution of the initial value problem. y" -…

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Q: H be the set of all points (x, y) in ℝ2 such that x2 + xy 3y2 = 3. Show that H is a closed subset of…

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Q: frequency 8 4 2 1 2 3 4 5 6 Do the data appear to be normally distributed? Explain. O Yes, the…

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Q: [21] (i) without finding B¹, the value of K for which KA-2B¹ + 1 = 0. (ii) without finding A¹, the…

A: Let A,B are n×n invertible matrices  and I is an n×n identity matrix. Then A.A-1=A-1A=I  I.A=A.I=A…

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Q: Obtain the general solution. (EXACT EQUATIONS) 2. y²dx = (xy - x²)dy

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Q: - [a C b If A = where a, b, c and d are real numbers, then prove that A²-(a + d)A + (ad-bc) I=O.…

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Q: (d) Apply the Squeeze Theorem to verify that lim x² sin I-0 (-1). = 0.

A: SQUEEZE THEOREM-:  Let  f , g and h be functions defined on an interval I . Suppose that for every x…

Q: Let Z₁, Z2, Z3 be the complex numbers such that Z3 - Z1 |Z₁-1|=|2₂-1| = |z3 − 1| and arg Z2 - Z1…

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Q: c) f(t) = sin tet d) f(t) = sin t

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Q: Find two linearly independent vectors perpendicular to the vector -Q. U=

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Q: Question 2 a) b) c) Given the region D enclosed by y² = x² and x² + (y+6)² = 18. Sketch the region…

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Q: 8. Find the centroid of the region bounded by y x and y = x².

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Q: or each of the following series, determine whether the series converges or diverges. (Sum from 1 to…

A: p-series Test : A series of the form ∑n=1∞1np is called p-series, its convergent when 0<p<1…

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.