1. Prove using vectors that the points (4, 3, 0), (2, 0, 1), (4, 1, -1), and (2, 2, 2) are the vertices of a rectangle. 2. Let Ā and B be nonzero vectors. Find k e R such that Ā + kB is orthogonal to B – Ā.

Q: Identify the open interval on which the function is increasing or decreasing. (Enter your answers…

A: topic - application of derivatives

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A: The course included parametric equation,polar coordinates, vectors ,sequences, Taylor expansion, and…

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A: Use derivative and critical point for finding the absolute maxima .

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A: The given functions are: x=t3+1, y=t2-t

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A: (-1)1/2= i

Q: Find recursive definitions and closed formulas for the arithmetic sequences below. Assume the first…

A: Given,2,5,8,11,14Here a0=2d=a1-a0d=5-2d=3we know that ,an=a0+(n-1)dan=2+(n-1)3an=2+3n-3an=3n-1

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A: I am attaching image so that you understand each and every step.

Q: ifind the Salution of thediffequ.

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A: Given problem:-

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A: Here we have to plot the graph

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A: The given matrix is:A=-11-21We need to find A-1

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A: This question is related to coordinate geometry ,we will solve it using given information.

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A: Follow the procedure given below.

Q: Find recursive definitions and closed formulas f sequences below. Assume the first term listed is 1.…

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Q: Q\ use Euler's method to the differen fial equa tion Solve y=XVXY When y co) =\ cnd

A: For the solution follow the next step.

Q: fined ely elx ex ex + e y.

A: y=ex-e-xex+e-xDifferentiate w.r.t x

Q: 2r –1 15. Evaluate dx. (x– 2)(x+1)' A) hx- 2| + hịx + 1| +C C) -hx – 2| + Inx + 1|+C B) hx- 2| – hịx…

A: To evaluate: ∫2x-1(x-2)(x+1)dx

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A: We can find the value of 'a' and 'b' as below

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Q: sinx 18. Supposed Ax) = [ V1+t* dt and g(y) = | f(x)dx , what is the value of g' 15 A) 2 C) B) D)

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Q: Use the Comparison Test to determine whether the series is convergent or divergent. Op Fur E n4/5 1…

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A: Solution is given below...

Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. 3n + 4 n= 1…

A: We will solve problems by comparison test.

Q: 14. Which of the following integrals is equivalent to cosxdx if u = V1- sin'x sinxV1- sin'x du c) ;…

A: We are asked to find equivalent integral to the given integral

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A: The given integral,      ∫012x+5x57dx Note:     Multiple questions are given, we are answer with…

Q: Use Theorem 9.11 to determine the convergence or divergence of the p-series. 1 1 + 1 1 1 16/2 * 81/3…

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Q: Find det A using the method of cofactors and the sign matrix. 2 2 6 A = 0-8 6 - 2 0 1 det A =…

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Q: 6-X Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

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