Does the piecewise-defined function S(x) = 5 if X < 2 and s(x) = 7 if x > 3 results in a well-defined function from R to R? Explain.

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Q: 31. Use Stokes' theorem to evaluate curl F. ds, where F(x, y, z) = −y² î + x + z²k and S is the part…

A: Given: F⇀x, y, z =-y2 i^+xj^+z2 k^ ,  x+y+z=1 , x≥0 , y≥0 ,z≥0. To find: ∬S curl F⇀·dS

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Q: 6. Use Laplace on the following: C. L'¹ (f(t)) f(t)= = 7 s5 (s²+16)

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Q: Question 39 1. Let A=MB (f) be the matrix associated with the linear map f(x,y,z) = (3x-y +…

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Q: Find the general solution to the following differential equation a. Xn+₁ = n +2 -X₁1 n +1 Xo = 1 2…

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Q: Let G be a finite group and let sym(G) be the group of all permutations on G. For each g in G, let…

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Q: 3 (d²x)². 7 2 y (dx)² + y ² (dx) ² + 3y || 5x

A: Order of a differential equation  The order of the differential equation is highest order of the…

Q: 5. Let D = {1, 2, 3, 4, 5}, C = {a, b, c, d}, and g = {(1,a), (2,c), (3,d), (4,c)}. Determine…

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Q: Evaluate the integral by reversing the order of integration. ર Solo ex dxdy=

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Q: 1. Let our domain be the natural numbers greater than 1. Define: P(x) = Q(x, y) = "x is prime" "x…

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Q: (a) Define ƒ (x) := √² -²/2 dt 0.45. √2π Using the Fundamental Theorem of Calculus, write down…

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Q: Plot the gradient vector field of f together with its contour map. (a) f(x,y)=4- -4-4-4 (b) f(x, y)…

A: Given:  a fx, y=4-x24-y24b fx, y=x2+y2 To Plot the gradient vector field and contour map.

Q: Provide 1 real-life situation involving  a) Rational Function b) Exponential Function Relate the…

A: To Find : real-life situation involving  a) Rational Function b) Exponential Function

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Q: 12. Consider the Laplace equation: uxx + Uyy = 0. Solve for u(x,y) on a square plate of size for the…

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Q: Find a table of values for each function and its inverse. a. f(x) = 3x + 1 Function f(x) X Inverse X…

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Q: By changing to polar coordinates, evaluate the integral where D is the disk x² + y² ≤ 36. Answer= (x…

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Q: Find the range of the following functions. a f(x) = 5x+1, domain (xe R. -5 ≤x≤5) b f(x)=4-2x, domain…

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Q: (a) (b) 72º (c) (d)

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Q: Question 19 Let f(x, y) = ety. What is the mixed partial derivative fay(x, y)? O ezy O (1+xy)ety…

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Q: 45 please

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Q: Problem II Consider a linear operator L: R4 → R4 defined by the formula below, where V₁ = (1, 1, 1,…

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Q: 1. Use Laplace transform to solve the initial value problem y" - 2y + 2y = tln(t) with y(0) = 0 and…

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Q: (Use the method of variation parameters to find the general solution of the differential equation 16…

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Q: Exercise 17.5.20. (a) Show that there is a well-defined function f: Z12 → Z₁, given by f([a]12) =…

A: (a) We are given that,        f([a]12) = [a]4     Now, let, [a]12 = [b]12               =&gt; a = b…

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Q: Use variation of parameters to solve the given nonhomogeneous system. *- ( ) - ( ) X' = -1 1 -1 +…

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Q: Show that fee-2 dz is independent of the path C joining the points 1 - mi and 2 + 3 mi and determine…

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Q: Multiple-Choice Tests   Professor Easy's final examination has 11 true-false questions followed by 2…

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Q: Let A = -8-2-26 6 4 20 18 6 and w= 3 -1 Determine if w is in Col(A). Is w in Nul(A)? Determine if w…

A: Given: A=-8-2-264618206 , w=31-1 To Check which of the following option is correct  (a) The vector w…