Find the values of the real constants a and b such that the function =-{ [ 1+ 2x + x²(5+ cos(1/x)) if x < 0, if x ≥ 0, f(x) is differentiable on R. a sin x + bcos x

Q: Let $K$ is a horizontal shear, next draw a vector $\vec{x}=\left[\begin{array}{l}x_1 \\…

A: Let be the transfomation representing vertical shear of the vector  .Then we have The above can be…

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A: The given series .The aim is to determine whether the series converges or diverges.

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A: Given points:Given functions:1) 2) 3) To find:The function which is best fit on each models.

Q: Consider the following second order differential equation: d²y dx dx² +5x + 16xy = 3x² with y(0) = 6…

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Q: 3. For f(x)=x²-2x+3, find the slope of the tangent line at the point P for which x=1 using the limit…

A: Here, y = f(x)              = x2 - 2x + 3Now, the slope of the tangent at P (for which x = 1) is…

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Q: Indicate whether the function f(n) is O (g(n)) but not (g(n), or • (g(n) but not O(g(n)), or •…

A: Given that Now, Recall  some Important  Result :1) 2)  3)

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Q: H find a second, linearly independent solution. The vector e²t 3 [F= -1 1 is a solution to x= x'.…

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Q: Give an example of a partition S of [-1, 1] that satisfies all the following requirements: •|S| = 5…

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Q: Let f(x) = √√√x, g(x) = x + 15 and h(x) = 7. Find the domain of the following fu on then simplify…

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Q: Solve the initial value problem. 3y' - 2y = e, y(0) = a Let ao be the value of a for which the…

A: A first order linear ordinary differential equation of the form  can be solved by using the…

Q: Problem 3. Solve the initial-value problem y" + y = 4 sinx, y(t) = 1, y'(T) = 2. All derivatives are…

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Q: A company manufactures a product at its plants in A, B, and C, then ships the product to six…

A: The problem is formulated in excel as below. The 2 images below show the formulation as well as the…

Q: 3. Produce a vector field using StreamPlot including the three initial conditions to produce three…

A: To produce a vector field using Stream Plot and visualize three initial-value solutions for the…

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Q: An initial amount, P₁ = $800, is invested at an initial rate of 3.6% for 7 years. a) Find the future…

A: (a)To find the future value of the initial investment when interest is compounded quarterly, you can…

Q: a) Write down a system of linear equations to describe the above problem. Hence, form a matrix…

A: (a)

Q: Find the flux of the constant vector field =-7-j+ k through a square plate of area 25 in the…

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Q: 10. In the contour plot below dark shades represent small values of the function and light shades…

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Q: An economist uses the model P(x) = -0.05x³ +3.25x² - 10x + 20 to estimate the price of a stock over…

A: The model  estimate the price of a stock over the next  years.The aim is to find when the stock…

Q: 70. Consider the matrix M = (ab) where a and c are real and b may be complex. If M can be…

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Q: 1. Determine the set of all z for which f(2)= is defined, and then write f(z) in u(x, y) + iv(x, y)…

A: 1. Determine the set of all  for which   is defined, and then write  in  form.

Q: Show that the set Q of rational numbers is countable.

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Q: A simplified economy consists of the two sectors Transportation and Energy. For each $1 worth of…

A: Since you have posted a multi sub part question according to guidelines I will solve first(a,b,c)…

Q: 1. Let ./ be an ideal of the ring R. Show that the ring R/J is commutative if and only if xy-yx € /…

A: 1) Let    be an ideal of the ring   Now, is  commutative     2nd part: Let  and   are  ideal  of…

Q: Let R be a ring with unity, and assume I has no nonzero zoro-dinzors, Lot a, bER and полгого assume…

A: Let R be a ring of unity, and assume that R has no nonzero zero-divisors. Let a, b ER, and assume…

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Q: The general solution of y' = 10 can be written in the form Y =C D

A: We are solving the given problem by using the method of separation of variable.

Q: Find all points on the curve r(t) = ti + t^2 j + t^3k where its tangent line is parallel to the…

A: The curve is represented by the vector function r(t)=ti+t2j+t3k .To find the points on the curve…

Q: Find all points on the curve r(t) = ti + t²j+t³k where its tangent line is parallel to the vector…

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Q: [3.49] The following is the current simplex tableau of a given maxin problem. The objective is to…

A: The current simplex table is as follows:RHSTo Find:a) Unknown a through g.b) Find .c) d) Is the…

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Q: The velocity of water, v (m/s), discharged from a cylindrical tank through a long pipe can be…

A: Given the equation that relates the velocity v(m/s) of the water and the time t(s) it takes to get…

Q: Let a₁ = B , a₂ = 圓 and a3 = The set {a₁, a2, a3} will span R³ unless h = 7.5 (If there are no…

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Q: Use Gaussian elimination to solve the following linear system. x+2y-z=1 2x+3y + 12 = 2 x+3y- 2z = 3

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Q: How does the Bellman operator apply to problems with discrete and continuous state spaces?

A: The Bellman operator is a mathematical tool that can be used to solve optimization problems in…

Q: Edwards Manufacturing Company purchases two component parts from three different suppliers. The…

A: The problem is formulated in excel as below. The 2 images below show the formulation as well as the…

Q: 1. Consider the matrix -6 07 6 2 3 0 3 2 Is the MR iteration guaranteed to converge for a linear…

A: The given matrix is:To find: Determine whether the MR iteration is guaranteed to converge for a…

Q: Which point is the polar of line AaP?

A: Given a plane with some lines.Point P is the center of Perspectivity.Aim is to find the polar of the…

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Q: a. a continuous function with an absolute minimum of -3 at x = -2 and a local minimum of -1 at x =…

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Q: The orthogonal projection of the point T(x,y) on a line of equation k: Ax+Bx+C=0 is a non-isometric…

A: The orthogonal projection of the point T(x, y) on a line of equation k: Ax + By + C = 0 is a…

Q: Write an equation for the graph shown using any coordinate system you'd like. Use x, y, z, r, theta,…

A: The given graph is:In the interval for the , the projection of the plot in the X-Y plane represents…

Q: e that a ball is dropped from the upper observation deck of the CN Tower in Toronto, 450 m above the…

A: Given that a ball is dropped from the upper observation deck of the CN Tower in Toronto, 450 m above…

Q: Does the graph represent a function that has an inverse function? No Yes

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Q: - Assume that Ā = (âx + ây + 2â₂) and that B = (âx − 2â₂) then find |Ã – Ē|:

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Q: Show that for every positive integer n, 5 divides 6″ – 1. Show that for every positive integer n, n³…

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