Let n P₁ P2 = ppp be the prime factorisation of an integer n > 1. 1: ti A 11. C.

Q: Using 1 - node Gaussian integration, we have f f(x) dx ≈ w₁f(x₁). What is the value of w₁ ? b+a (a)…

A: Given that using 1-node Gaussian integration, we have…

Q: Q2): A polluted lake has an initial concentration of a bacteria of (1*107 part/m³), while the…

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Q: Q3): A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a…

A: To find: Value of f(5.00) Using Lagrange interpolating Polynomial Rule.

Q: II. Find Do not simplify your answers. dy dx tan-¹(cosh.r) 2. y= (sin²x) (sech x)sec z [use…

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Q: solve the linear system below  a+2b-c+4d=6 -a-4b+2c+2d =4 2a+2b-c+2d =4 a+2b+c = 4 using…

A: The given linear system is a+2b-c+4d=6-a-4b+2c+2d=4 2a+2b-c+2d=4  a+2b+c= 4 A. We will solve the…

Q: . Given the matrix A below, alue for det in A A = 1 0 2 2 0 0 2 1 1 10 1 0 1 4

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Q: 2. Use Squeeze Theorem to evaluate lim sin(sinh x) esch z. 8118

A: Squeeze theorem: If f(x)≤g(x)≤h(x) for all x and limx→af(x)=limx→ag(x)=L then limx→ah(x)=L…

Q: The function f (z) = |z|+1 O True O False is analytic

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Q: 2. Use sketches of regions or number lines to show each pair of equivalent fractions: a. 10 15 95

A: Given :Fraction :                      23 =  1015

Q: Solve the following Initial Value Problem using Laplace transfo -9t y" - 12y + 11y = e ;y (0) = 1,…

A: The given equation is y''-12y'+11y=e-9t Taking Laplace transform on both sides Ly''-12y'+11y=Le-9t…

Q: V. Given: el3r-6-2, if x ≤2 13 f(x)=[2x - 5], if 2 3 √x²-9, 1. Determine if f is continuous or…

A: Given function is fx = e3x-6 -2   if  x≤22x-5  if  2<x≤3x2 -9  if  x>3 Domain for f(x) = -∞, ∞…

Q: Using Gaussian integration, (a) 2 ¹₁ f(2x + 3) dx (c) 3 ¹₁ f(3x + 2) dx the integral ff(x) dx is…

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Q: Find A where R is the region R outside the circle r=2 and inside r= y sin o

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Q: 6x-25x+8x+43x--8x-12 (3x4-11x3 +9x²-11x+6) (9x² +12x+16) + C(3x+2)+D 9x²+12x+16] Find f - [Ax+B x²…

A: Given integral is      (1) Its reduction is ∫Ax+Bx2+1+C(3x+2)+D9x2+12x+16dx We can write it as…

Q: VIII. Suppose that f(x) is continuous everywhere and the graph of f'(x) is shown below. Do not…

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Q: Find the solution of non linear partial differential du equation ди = U бу dx

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

A: The given system is: 6x+3y+2z=66x+4y+3z=020x+15y+12z=0 To find: Inverse using Gaussian-elimination…

Q: Q3): A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a…

A: Newton Method:-  so the value if y at x=5.00 is 6.28 inch

Q: y" - zy' +y = e²+t₂ y(0) = 1 y'(0) = 0, look for y(t) by Laplace Transform?

A: The solution is given as

Q: (ix) = (hang R. y=x and y=x²

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Q: 4: 4d³y - 13+6y=0 dx3

A: Given differential equation: 4d3ydx3-13dydx+6y=0To find: General solution of the differential…

Q: (1.5) Investigate the complete controllability of the linear autonomous system J=-2y+u y=-x+y in the…

A: Given,x˙=-2y+uy˙=-x+yTo find: Controllability if-            a) the control u is unbounded…

Q: Suppose that the demand function of a product is given by where p= (30-x)1/2 P is the unit price and…

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Q: x: 1 f(x): 1 cubic spline interpolation for the data : 2 3 4 5 0 1 0 1

A: We need to find cubic spline interpolation of given data.

Q: -1<x<0 swer only three for the following function f(x) = { x: 0<x< 1 Find the Fourier coefficient…

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Q: Consider the matrix

A: Given, the matrix                A=0-3-1020233 And the eigenvalues of A are λ=1, and λ=2.

Q: Write the following English sentences in symbolic form- 1. Birds fly if and only if sky is clear.…

A: We have to write the given sentences in symbolic form.

Q: Find the solution using Variation of parameter. (D²1)y=e* + 1 1 y=C₁e* + C₂e-x+ 를xex ex-1 2 4 1 1 -X…

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Q: Solve the following PDE by using Laplace transform du du + əx əx =-u; x > 0.t> 0 with boundary and…

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Q: Test the convergence of the power series below: (-2) n Σ 3n-2(3x-5)n n=1

A: Radius of converges of the power series

Q: 5. Find all values of k for which A is invertible. [k A=0 Lk -k 3 k+1 1 -8 k-1.

A: As per guidelines I have solved the first question i.e.questions no.5 if you want solution of other…

Q: Let f be an arithmetical function (not necessarily multiplicative). Prove that there is a…

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Q: What is the missing number? * 15 17 8 9 8 12 27 40 6 3 28 2 12 23 13 ? 28

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Q: [MO23] For the function y = cos x + sin x, determine its a. MacLaurin Series expansion up to fifth…

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Q: V. Given: 2. Find f'(2), if it exists. el3r-61-2, f(x)=[2x - 5], √x²-9, if x ≤ 2 if 2 3

A: Given that  fx=e3x-6-2,if x≤22x-5,if 2&lt;x≤3x2-9if x&gt;3

Q: Example 10.25. Solve the initial value problem dy/dx=x-y², y(0) = 1 to find y(0.4) by Adam's method.…

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Q: Consider the following matrix: 3 40 80 70 A=0 2 0 3 0 2 0 1 3 4 0 10 0 70 6, (a) Find a basis for…

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Q: Matrices D, M and X are 5 x 5 invertible matrices. Given det (A) = 7, det (M) = -4, and Hlet (P) = 6…

A: (a).  det3MT As  detMT = detM So det3MT = 35detM = 243(-4)  =  -972 Hence Answer: det(3MT) = -972

Q: Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an…

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Q: uppose h' is continuous at x = 0 and h'(x) = Find h"(0+), if it exists. tan(2x) — 1 if x > 0.

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Q: log: (x+3) 2-1-1-cosh(cos-¹x) 4. lim

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Q: lowing vector in the span{V₁, V₂, V3}? 8,9) me vector is in the span. me vector is not in the span.

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Q: Solve using the undermined coefficient of differential equation

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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: Which of the following series is converge or diverge - ΣΤ' ,0.7777777777777 n2 n=1 . Σ{} 27

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Q: V. Given: 2. Find f'(2), if it exists. el3r-6-2, f(x)=[2x - 5], √x²-9, if r ≤ 2 if 2 3

A: Given fx=e3x-6-2,if x≤22x-5,if 2&lt;x≤3x2-9,if x&gt;3

Q: PROBLEM: Derive the z-transform for f(t) = sin oot u(t). z¹sin(@T) ANSWER: F(z) : = 1-2 z ¹ cos(@T)…

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Q: Solve the differential equation: (D² + 1)y = tan x

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Q: k рех, у) хсу. y = 1,2,3 other - and the marginal probability function of Y P (Y) 6

A: Given PDF is p(x, y) = kx2y,x=1, 2,  y=1, 2, 30,otherwise

Q: [ e2x+lnx’ sin x dx = + ½ fe²x cos x² dx

A: