Consider the piecewise function 2+x² x<0 x=0 g(x) = 1, 2-³, 0

Q: Example 8.25. Evaluate x + 2x + 1 Jo 1+ (x + 1)². dx by Gaussian 3-point formula.

A: Gaussian 3-point formula. variable change x=a+b2+b−a2v if ∫abg(x) dx=b-a2∫-11g(a+b2+b-a2v)…

Q: Example 10.20. Using Milne's method find y(4.4) given 5xy + y²-2=0 given y(4) = 1, y(4.1) = 1.0049,…

A: Solution : Given, 5xy'+y2-2=0 ⇒y'=2-y25x Table of x and y x 4 4.1 4.2 4.3 y 1 1.0049 1.0097…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5) 2=2y, the…

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Q: 2 Example 10.8. Using Euler's method, find an approximate value of y corresponding to x= 1, given…

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Q: The linear transformation Z: M2x2 (R)→ M2x2 (R) satisfies z = [₁₁3] ² [²D=[²₁²] ² D=[¹² 1. Solve for…

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Q: (a) Consider the following differential equation, 2y' + 3y − 12xy¾ = 0, y(0) = 1. (1) (i) Consider…

A: NOTE:Kindly repost the other question as a separate question.

Q: 3:Use Gamma & Beta properties to evaluate : f (In x)³ dx

A: The gamma function is Γ(z)=∫0∞e-ttz-1dṭ The Gamma function is a non-integer generalization of the…

Q: Pandas are an endangered species. Currently (2021) their world-wide population is 3,500. Their…

A: As per company guidelines i am solving first three sub-parts. The exponential decrease is defined by…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)^2 = 2y,…

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Q: ds dt dQt dt dP dt = μ-μP-BPS, :-(µ + y) S + BPS + αSQ₁ = = −µQ₁ - αSQ₂ + y(1-0) S.

A: As per the question we are given a population model in terms of dynamic system. And we have to find…

Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

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Q: 3.) x + y + z = 6 y + 3z = 11 x - 2y + z = 0

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Q: INTEGRATION OF STANDARD FORMULAS. Note: Please don't use NEED ALSO SOLUTION PER ITEM OR NUMBER. 2.…

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Q: A student has measured a solution using a graduated cylinder of 2.0 Litres. The uncertainty of the…

A: The error in measurement is unavoidable due to certain reasons, so the percent error provides the…

Q: Solve the following system of nonlinear equations 2x₁x₂2=0 x₁² - 4x₂ -4 = 0 Using the fixed-point…

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Q: Consider the following game and the direct correlation device. Show that the device is a correlated…

A: Solution:As we can see that A1  is the best response to P1's arrangement, though P2 is best response…

Q: properties to evaluate : 8 (In x)3 dx

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Q: A ball is thrown from an initial height of 5 feet with an initial upward velocity of 35 ft/s. The…

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Q: Let S be the solid inside the sphere p = 6cosø and below the cone Ø = n/4 Set-up the iterated triple…

A: We will convert equations from spherical to cartesian co ordinate system and then find limits for…

Q: Determine whether the given linear operator/matrix is diagonalizable. (a) T : R³ → R³ with T(1, 1,…

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Q: bikes on sale at $599.99. At the sale price, 18 bikes were sold during the one week sale. (a) What…

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Q: Simplify a(a+1) (a+b)(a+b+1) a² (a+b)²

A: LCM is an abbreviation for "Least Common Multiple." The smallest number that can be divided by both…

Q: › affine space (E‚È‚+), let (ai)ie is linearly independent for some i

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Q: retail store estimates that weekly sales s and weekly advertising costs x both in dollars are…

A: Given that a retail store estimates that weekly sales s and weekly advertising costs x both in…

Q: QUESTION 13 Calculate the area of the smaller region (to the left of the parabola) bounded by (x+…

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Q: Express all answers as decimals rounded to 3 decimal places, if needed. Express percentages decimals…

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Q: Find the area bounded by the curve 4 square units 8 square units 16 square units 10 square units =…

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Q: Example 10.22. Using Runge-Kutta method of order 4, find y for x = 0.1, 0.2, 0.3 given that dy/dx =…

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Q: A trough is full of liquid of weight density 9,000 N/m3. The ends of the trough are equilateral…

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Q: 2: Find the first 4 terms of the Taylor series for: f(x)=sin лx near a=0.5

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Q: Use a software program or a graphing utility with matrix capabilities to find the transition matrix…

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Q: Prove that the following graph does not contain a Hamilton cycle. a b с d h g e m k

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Q: Question 20 Evaluate ·S= A B C D 3x5 3x4+6x3-3x2 - 6x x+In[ + In -dx. using method of partial…

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Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

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Q: in extension of a fie elements in K which ver F from a subfie

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Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

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Q: Using the power series method about x = 0, the recurrence relation of the differential equation: y"…

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Q: QUESTION 19 The volume of the solid generated by revolving the region bounded by x2 = 4y method. The…

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Q: Example 9.14. Solve yy + (x + 2)y + xy + x² + 2x + 2 = 0.

A: Please find step by step solution below:

Q: Question 2 A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are…

A: We will find force on a horizontal slice of trough and then integrate it to find total force on it

Q: Sketch the region of integration and set up iterated integrals for both type I and type II orders of…

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Q: Let K be an extension of a field F and let f(x) € F[x] be a polynomial of degree n≥2. Then a€K is a…

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Q: @ For the following power series expansion, give the anter and find the redive of convergence Test .…

A: Follow the steps.

Q: Suppose we want to choose 6 colors, without replacement, from 13 distinct colors. (a) If the order…

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Q: 4. Given these data X 1 2 3 5 f(x) 3 19 99 Calculate f(4) using Lagrange polynomials of order 3. 7…

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Q: 4 Which of the following is true for the integral A. In 5-In(-2) B. In 5-In 2 C. -In 5 + In 2 D. In…

A: Solution no. (2)  Options (B) is correct

Q: Use spherical coordinates to evaluate the integral •√₁-x² √√₁-x²-x² (x² + y² + ²)dzdydx.

A: To evaluate the integral using spherical co-ordinate system :-

Q: Use Simpson's Rule to evaluate the following. n = 10 3 1 dx -3 1+x²

A: Simpson's 13 rule: ∫abydx=h3(y0+4(y1+y3+y5+...++yn-1)+2(y2+y4+y6+...+yn-2)+yn), where h=b-aN and N…

Q: 3. Make drawings on a separate page to show your calculation a. I have R249.50. Tickets cost R10,00…

A: # as per the guidelines we are entitled to solve one question(maximum three subparts) at a time,…

Q: Evaluate the following definite Integrals by using Gamma or Beta Functions: 5 (a) [√4x In (V√x)] idx…

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