Problem 2 Let f: [a, b] → [a, b] such that f(x) − f (y)| < |x − y for all a ≤ x ≤ y ≤ b. Prove that there exists ce [a, b] such that f(c) = c.

Q: If log \_(2) 32 = 3x - y, which of the following is true? y=3x+ x = (1) / (3) * y + 5y = - 3x + 5x =…

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Q: · x”+ 4x' + 5x = 8(t − ñ) + d(t − 2π); x(0) = 0, x '(0) = 2

A: L{ sin(at)}= 1/(s²+1) L{f(t-a)u(t-a)}=e-asF(s) L{y'}=sY(s)-y'(0) L{y''}=s²Y(s)-sy(0)-y'(0)…

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Q: Use Bisection Method to approximate: √786, accurate to within 10-3

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Q: K) Find the volume of the cone √² + y² ≤ z ≤ 4. (Use the formula for the volume of a cone to check…

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Q: Can you please recheck the solution

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Q: Fast pls solve this question correctly in 5 min pls I will give u like for sure Sini Questions is…

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Q: 7. Suppose à = i + j, b =j + k. The angle between vectors à and bis

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Q: I made a mistake in A, the correct is: A) Given four points A,B,C,D such that A*B* C and A*C* D:…

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Q: $G ܀ G2$ ܀ = = +ܐܨ 10 10*1 3.25 10 3.25 10 + 3 250 10 10+1. + 10 10+1 3 250*10 10*1 S S = = 1…

A: Given  G1s = 1s2+0.337s             ⇒    G1s = 1ss+0.337 = as + bs+0.337…

Q: 16. Calculate ]] (V × F) · în dS, where F = (y, −x, e²²) and S is the part of paraboloid z = 3x² +…

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Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

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Q: Integrate f (x, y) = y over the top half of the circle (x − 1)2 + y2 = 1 in two ways a) In…

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Q: 17. xy' = √√√1 - y², y(1) = 0

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A: Given fx = π+xif  -π &lt; x &lt; 0π-xif   0 ≤ x ≤ π               The Fourier series of  fx…

Q: y' = x² y (2 + x³) y(0) = −2

A: The given differential equation is       y' = x2/{y(2 + x3)}   =&gt; dy/dx = x2/{y(2 + x3)}   =&gt;…

Q: Solve the initial value problem. X - [3 -1³]X, X (0) - [!] XI= = 5 = e2t 9 cos(8t) - 9 sin(8t)]…

A: (.)  The given system is ,       X' =  3-135   1X  ;   X(0) = 15 We find eigen value of matrix…

Q: The graph of f is given below. 6+ 5 4 3 2 -6 -5 -4 -3 -2 -1 -1 -2 -3 f(x)dx + [ f(x)dx= Lo f(x)dx…

A: Since you have asked multiple subpart question, we will solve the first three subparts for you, as…

Q: Find the centroid of the thin plate bounded by the graphs of g(x)=x² and f(x) = x + 6. Use the…

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Q: Use the improved Euler's method to obtain a four-decimal approximation of the indicated value. First…

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Q: Compute the length of the curve r(t) = = (2t, In(t), t²) over the interval 1 ≤ t ≤ 8. (Use symbolic…

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Q: a. Use the given Taylor polynomial p2 to approximate the given quantity. b. Compute the absolute…

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Q: For the matrix A = 1 -2  4  , what is the value of | A| ?                               2  0  6…

A: Given, The matrix A = 1-24206373   We have to find the value of A.

Q: ← In order to accumulate enough money for a down payment on a house, a couple deposits $360 per…

A: I have explained everything with in the solution .please go through that.

Q: 33 38 30 68 69 36 71 72 46 79% at is the mean? Select the correct choice below and, if necessary,…

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Q: (a) sec² (In x) Calculate the following indefinite integrals. dx X I (b) √ √√t VEFI + dt

A: This question is about to evaluate indefinite integral.

Q: Given: -0-0-0-0-0 Question: Is vector w in the subspace spanned by vectors u₁, U2, U3, and u4? Show…

A: The given vectors, u1=-1-23-6, u2=2-124, u3=-2-316, u4=-1331, w=-1112. We have to check the vector w…

Q: 5 + 15 + 45 + · · · + 5 · 320. 230 330. .Q.Find b. Find 1 – 3 + 3 -+- +

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Q: 2. See the following problem: Justify all solutions (give English explanations as you answe y' =…

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Q: The given matrix determines a linear transformation T. Find all x such that T(x) = 0. 4-2 6 -7 5-9…

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Q: Problem 5. and Define transformations 7 and p on R² = {(x, y): x, y = R} by T(x, y) = (y,x) p(x, y)…

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Q: Knowing that arctan(1/sqrt(3)) = π/6, use the maclaurin series of arctan(x) to approximate π with an…

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Q: Problem 5. and Define transformations 7 and p on R² = {(x, y): x, y = R} by T(x, y) = (y,x) p(x, y)…

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Q: Find the Fourier Sine Series for the following periodic functions f(x) = x 0<x<π f(x) = x 0<x< 1

A: Let a function f(x) is defined over an interval (0,L). Then its Fourier Sine Series expansion is…

Q: Could someone explain the gram schmitt process in linear algebra? One example I'm having trouble…

A: Gram-Schmidt Process:                                     Let  x1,x2, .....,xn be the linearly…

Q: 9. Use Laplace to solve the system: dx dt dx dt x(0) = 0, y(0) = 0, y'(0) = 0, y"(0) = 0 -4x+ d³y =…

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Q: 2. Finite, abelian (and additive), not isomorphic to Z2 or Z2 x Z2, and also for every element a,…

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Q: Eliminate the parameter for the following set of parametric equations. Sketch the graph of the…

A: The parametric equation of curve x(t)=1+3t   _____(1) y(t)=3-6t+t²   _____(2)

Q: Find the matrix A' for T relative to the basis B'. T: R3 → R3, T(x, y, z) = (y + z, x + z, x − y),…

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Q: Find the work done by the force field F in moving an object from A to B. F(x, y) = 6y³/2 i + 9x√yj…

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Q: Now explain why we may choose eigenvectors V₁ for ₁ and v₂ for ₂ that each have unit length and are…

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Q: Sketch the even 2π- periodic extension and find the Fourier Cosine Series of the function f(x) given…

A: Given  fx = xif  0 &lt; x &lt; π2π-xif  π2 &lt; x &lt; π            The Fourier…

Q: 3. A thin plate (or "lamina") occupies the region bounded by the graphs of y = x² and x = 4y². This…

A: The given region is bounded by y=x2, x=4y2 The density is ρ=20 gm/cm2

Q: Sabiendo que arctan (1/√3) π/6, use la serie de Mclaurin de arctan (x) para -6 aproximar π con un…

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