Show that for all real x sin x 1 sin²x x + sin³ x x + 2 sin x 2 + sin x

Q: The integral S dx √x(1+x) is improper for two reasons: The interval [0, ∞) is infinite and the…

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Q: The cash-flow diagram is provided. a. If P = $2,000, A = $200, and 7% = 9% per year, then N= ? b. If…

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Q: Let f(2)= iz³ + cos(z²) z² +1 i. Find f'(z). ii. Evaluate ƒ'(–2i) and simplify. iii. State the…

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Q: II. Given: sinh r − 1 if x 2 x-2 Determine if f is continuous or discontinuous at x = 0 and at x =…

A: Jump discontinue of the function

Q: The regular price of a color 441.87 During a sale, Hill TV is selling the TV for 358.12. Determine…

A: Solution

Q: Here are three second-order differential equations with initial conditions: c) x(t): - 3x + 2x = Zet…

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Q: Construct the truth table of (p ^ q) V ~ r

A: the truth table for the given expression is

Q: Find an equation of the surface of revolution by revolving the plane curve 3y = √(9- [(x-1)] ^2)…

A: Given:3y = (9-(x-1)2)

Q: 2. Using the fact that D₁ ((2 − x)−¹) = (2 − x)-², find the Maclaurin series for 4x³ f(x) = (2 -…

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Q: Find the first five non-zero terms of power series centered at x = 0 for the function representation…

A: We have to find the first five non-zero terms of power series representation centered at x = 0 for…

Q: Homework of differential equation Q₁: Solve the following differential equations a) xy' y'= x² + 2y…

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Q: Directions Create a graph where the vertices are the following colleges and universities. • lowa…

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Q: Consider the plane region to the right. Using trapezoidal rule (2 intervals), Estimate the area of…

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Q: Consider the function f(x) = 12, x = [0, 2]. Construct the Lagrange interpolation polynomial which…

A: Given function is fx=x21+x2, x∈0,2. We have to construct the Lagrange's interpolation polynomial…

Q: Using 4-node Gaussian integration in approximating ³x ex dx, which In 3 f(x) in the formula has…

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Q: Explain why you think the series n=1 converges to a finite number n+1 or diverges. If the series…

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Q: Show that the equation 2²y Əy +2k 2²y 6x² ax² 1 2² Ət possesses solutions of the form X 00 kt Σ c,…

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Q: Find the eigenvalues of the triangular or diagonal matrix. (Enter your answers as a comma-separated…

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Q: Identify and draw a sketch of the surface [(x-2)] ^2/9+ [(y-3)) ^2/4- 【(z-1)]^2/36=1 O elliptic…

A: We will generalize the equation and then identify the type of surface  Elliptical hyperboloid of…

Q: 1. For the following directed graph, find the shortest path from note 1 to note 9. Please show each…

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Q: Example 7.22. Find the distance moved by a particle and its acceleration at the end of 4 seconds, if…

A: Legranges interpolation

Q: 7) A fair coin is flipped three times. Events A and B are defined as: A: there are at least two…

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Q: Approximate the area of the region enclosed by y = -x² + 4x and x-axis using trapezoidal rule with 8…

A: Given y = -x2 + 4x h = b-aNh = 4-08 = 0.5

Q: dy + 4 (X-11² Y = X+1 cos y dx + (x Siny - cos²y) dy = o 0 9. (x-1)³ [X-11³

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Q: 2TT Ex. 5/14.2 sindy dx 0

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Q: Calculate the divergence and curl for the following vector fields. Describe the characteristics of…

A: for a vector field F=P,Q,R Divergence  DivF=Px +Qy +Rz Curl of F =i^j^k^∂∂x∂∂y∂∂zPQR Divergence…

Q: 7-Write three examples about sketch the graph in polar coordinates from families of circles

A: A circle in polar coordinates is given by the formula, r=acosθ and r=asinθ where, a is the diameter…

Q: Let G=(V, E) be a graph such that • V| ≥ 3, G has exactly 2 leaves, and in G all the non-leaf…

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Q: A square matrix A is nilpotent if A" = 0 for some positive integer n. Let V be the vector space of…

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Q: prove that 01a| = 0 => a=o @ 1-al-lal @lak b ⇒-b<a<b @la-bla lal-lb/

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Q: Consider a bounded function f [a, b] → R and a partition P = U(f, P) ≥ U(f, Q) and L(f, P) ≤ L(f,…

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Q: f(z) = cos(C * z)

A: Here we use the property of the analytic function.

Q: Let I = [0, 1] be the unit interval. Construct a sequence of closed sets A₁ 2 A₂2 A3... in the…

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Q: Draw  (i) a simple graph,  (ii) a non-simple graph with no loops

A: (i). Simple graph:      A simple graph is a graph that does not contain more than one edge between…

Q: xy'=y+ IX2-y2 ху

A: We have to find the general solution of the given differential equation xy'=y+x2-y2 .

Q: /2 [u log (a cos 0+b² sin³ 0) de- log a+b GREGORIA 2 a>0, b>0.

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Q: A fixed point of f is a value of x that satisfied the equation f(x) = x; it corresponds to a point…

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Q: Consider the following matrix: 3 4 0 8 0 7 0 4 A=0 2 0 3 0201 3 4 0 10 0 70 6, (a) Find a basis for…

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Q: Sketch the region bounded by the graph of the equations and find the area of the region. x = y² -…

A: Solution

Q: For the following linear system, find the inverse of the coefficient matrix using Gaussian…

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Q: 5. (a) Evaluate the polynomial y = x³ - 8x² + 12x - 0.45 at x = 2.378. Use 4-digit arithmetic with…

A: (a) The objective to evaluate the polynomial p(x)=x3-8x2+12x-0.45 at x=2.378. Use 3-digit arithmetic…

Q: Use Djikstra’s Algorithm - Query ) What is the shortest path from A to G?

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Q: 9. Using integration by parts, Then k is? (a) - 1.5136 [*²x³ cos(x²) dx = k − [*³x sin(x²) dx -…

A: Given integral is ∫02x3cosx2dx

Q: Some value of f(x) and ƒ'(x) are given in the table. If no value is given, then you should assume…

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Q: Marie and Danny Would like to buy a house for $220,000. The down payment for the mortgage is 30% of…

A: Given, Price of house is $220,000. The down payment for the mortgage is 30% of the price of the…

Q: 15-46. Graphing functions Use the guidelines of this section to make a complete graph of f. 31.…

A: We have to draw the graph of given function.

Q: For a full-rank matrix A element of (R mxn) , where M<n and b element of (Rm), find the stationalry…

A: We have to use the Lagrange method with multiple constraints in order to minimize x22 subject to…

Q: Use Newton's method to approximate all the intersection points of the following pair of curves. Some…

A: we have y = 36x and y = x2+4 36x = x2+4 x2+4-36x = 0 f(x) = x2+4-36x f'(x) = 2x-18x-12 = 2x-18x

Q: Q2: 1. Solve the following equation exactly ý + 2xy = x and y(0) = 1.5, h = 0.1 2. Use the Euler…

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Q: Let 8 = {(1, 1, 0), (0, 1, 1), (1, 0, 1)} and 8' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)) be bases for…

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