Example 14. Given the function S x + a?, f (x) = if x < 0 a cos x + B sin x if x > 0, find the real constants a and B s.t. the function f is continuous and differentiable at x = 0.

Q: 2. Find the order of growth of the following entire functions: (a) p(z) where p is a polynomial. (b)…

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Q: 15. Find the largest root of x - 4x + x² + 1.2 = 0.

A: Newton's Raphson method

Q: b +c c+a a + b a b c Show that 9 +r r+p y + z z + x 2| р 9. r %3D x + y х у z

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Q: Gaussian Elimination x - 2y + z = 0 2x + y - 3z = 5 4x - 7y + z = -1

A: Given system is  x - 2y + z = 02x + y - 3z = 54x - 7y + z = -1

Q: In Lxercises 7 through 12 use a fixed point iteration scheme to find the required roots. 7.…

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Q: If C = {x: x2 + 11x + 30 = 0,x E N}, then C is a/an? Empty set Infinite set Finite set None of these…

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Q: Find the solution. (D2 - 2D - 3)y = 0; when x = 0, y = 0, y'= 4 A y = -e-3x – e 2x (B y = e¯+e3x y =…

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Q: Need typed and correct solution otherwise will get down vote Every Eucledean domain is a PID (with…

A: Given, Every Euclidean domain is a PID. Now we will proof this therorem.

Q: A space vehicle flies into a gravitational force field F(x, y, z) = -y(b²x² + a²y³) i+ x(b°x² +…

A: Introduction: The line integral is used to determine the work done by a vector field. If the vector…

Q: Determine whether the given specification is consistent or not. 1. The student either has…

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Q: 36-40. How many distinct permutations of the word "statistics" begin and end with the letter "s"?…

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Q: Find the volume of the solid when the area contained by y = x² and y = x* is revolved around the…

A: Volume bounded by regions

Q: Q1:The following vectors; Ā =, B =< 2,-4,6

A: To find the cross product of the vectors  A⇀×B⇀=ijk14-12-46 simplify…

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Q: 111111 is prime. Prove that, in any radix b, The number 11111 (11...1), can be prime only if the…

A: As per the question we have to prove that the number 111...1 containing n number of 1's will be…

Q: 6. Fill in the blanks Let y(x) be the solution of the initial value problem: y" = 16, y(0)=1 and…

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Q: 325= (100 x ____) + (10 x _____)

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Q: Statins are used to keep cholesterol in check and are a top-selling drug in the U.S. The equation: S…

A: Given, S- 1.9x = 4.5 Where S is the amount of sales in billions of dollars and x be the years after…

Q: is transformed to the diagonal form D= 1"'AT, where h b The matrix A= %3D cos 0 sin0 T= -sin 0 cos0…

A: Given matrix is A=ahhb and diagonal matrix is D=T-1AT where T=cosθsinθ-sinθcosθ Now…

Q: a h is transformed to the diagonal form D=T'AT, where h b The matrix A = cos 0 sin e T = - sin e…

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Q: Consider the space P2 and consider the vectors B ={ 1 + 2t +2t2, 3+5t +3t2,-2-3t} and C = {1,t,t2}.…

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Q: H.W: find the local maxima, local minima, and saddle point of the functions: 1. f(x, y)= x² + xy+ y²…

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Q: 5 6 0 4 0 0 0 0 -1 -2 7 3 A = (2) 1 1. The matrix A can be decomposed using partial pivoting as PA=…

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Q: 4) Find intlection points ot the dollowing tunetions. X-1 X-2 X+1 .

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Q: Apply Parseval's identity to the function f (x) = x, - nSxSn and deduce that n16 = 1/12+1/22 + . +…

A: For the solution follow the next steps.

Q: Find the number of different signals that can be made by arranging at least three flags in order on…

A: find different signals

Q: The following differential equation y' -xy2 is x2y+y? Separable Homogeneous This option This option…

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Q: Suppose x ~ Uniform(1, 2), and

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Q: Let X have pdf f(x) = e-X /(1+ e -X)2 −∞< x < ∞ Show that Y = 1/(1+ e -X)has the uniform…

A: The complete solution is in given below

Q: 2i n. 19. Which of the following definite integrals is equivalent to the Riemann sum lim 2- - dx C)…

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Q: Let the matrix below act on C2. Find the eigenvalues and a basis for each eigenspace in C2 3 - 3 3 3

A: The given problem is to find eigen values and corresponding eigen spaces of the given 2*2 matrix.…

Q: Determine the domain and range of the function using the graph below: 15- 14 13 12 10 6- 4 2 -5 -4…

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Q: Tutorial Exercise Use the shell method to set up and evaluate the integral that gives the volume of…

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Q: Solve for remaining parts of the given right spherical triangles below. Given the right spherical…

A: note : As per our company guidelines we are supposed to answer ?️only 3 sub-parts. Kindly repost…

Q: QUESTION 3 3 Given the double integral, e dxdy. 0 3y

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Q: (D2 -4D +7)y = 0 A y = e²"(c,cos/2x+c,sin/2x) COS y = e2"(c,cos/3x+c,sin/3x) В © y = e (c…

A: 1. Given differential equation is (D2-4D+7)y = 0 Here Auxiliary equation is D2-4D+7 = 0⇒ D = 4 ± 16…

Q: Use Simpson's rule with n = 18 to calculate the circle's area, which is specified overhead by f(x) =…

A: Given: The circle, which is specified overhead by fx=3-x2 and beneath by gx=-3-x2.   To calculate:…

Q: Equations Solve: dx + y= sin t dt dy where y (0) = 0, x (0) = 2 %3D + x = cost dt

A: Solution of system of Linear equations

Q: Laplace equation is called a harmonic function. Let the functions u = u(x, y) and v = v(x, y) be of…

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Q: prove that the gcd of the final values for x and y equals the gcd of original x and y in Euclid’s…

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Q: Find the Maclaurin series of e²° and its interval of convergence. Write the Maclaurin series in…

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Q: Find the general equation of the plane perpendicular to the line z – 2 y + 4 1- x = 3 and is 3…

A: We have to find the equation of plane.

Q: SHOW THE SOLUTION OF: (1+t?)ds + 2t(st? - 3(1+t?)2 dt = 0; when t=0, s = 2

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Q: 29. Dario puts 44 marbles in a box in which 14 are red, 12 are blue, and 18 are yellow. If Dario…

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Q: How many members of the Mathematics for All Club submitted their ballots?

A: (AJB),(JAB),(BAJ), (BJA) are disjoint sets  then there are 6 permutations. so the others two…

Q: A company that produces ribbon has found that the marginal cost of producing x yards of fancy ribbon…

A: From the given information, the total cost can be determined as ∫01000C'xdx. That is,…

Q: Find the eutre me points of the Following Function.

A: Maxima minimum of the two variables

Q: Show that J, (z cos0)d0 = - R/2 os e)de = 1-cos z %3D 21

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Q: Use haplace transforms and partial fractions to so lve y" + 2y'+10y=Uş(t), y(0)=3,y'lo) =-8

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Q: Find the volume of the parallelepiped (box) determined by u, v, and w. u V w i+2j 2i - 2j + 3k 2i +…

A: The given problem is to find the volume of the parallelepiped determined by given vectors. u=i+2j…