1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the vertices of a parallelogram.

Q: Use the Quadratic Formula to solve the quadratic equation. (Enter your answers as a comma-separated…

A: Given the quadratic equation is 32x2 - 6x + 9 = 0

Q: 9xdx 1 9xdx D=

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Q: fined ely elx ex ex + e y.

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

Q: A particle moves along the x-axis such that at any time t 0 its position is ax(t), its velocity is v…

A: The velocity of a particle at any time t is given as: vt The acceleration of a particle at any time…

Q: H.W: find the local maxima, local minima, and saddle point of the functions: 1. f(x, y) = 2xy- x² -…

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

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

Q: Use the graph to estimate the open intervals on which the function is increasing or decreasing. Then…

A: Please refer to the image below

Q: Evaluate the integral of the volume of the solid formed by revolving the region bounded by x² + y =…

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Q: Use the graph to estimate the open intervals on which the function is increasing or decreasing. Then…

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Q: Test for convergence or divergence, using one of the tests listed below. 4 n3 - 343 n = 8 O…

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Q: -(-3у?-у-2)dy 2y3+y2+4y

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Q: Use long division to divide. (Simplify your answer completely.) (9x – 4) ÷ (3x + 2) 2 3

A: Here we will use long division method,

Q: x*+1 dx = 0 y

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Q: Solve th D.E using Exact dx +(x² +3y* )dy

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Q: 30 20 10 -10 - 6 4 -2 8 10 -10 -20 30 16

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Q: Find the degree and leading coefficient for the given polynomial.   −2x2−7x4+x−8 Degree: Leading…

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Q: Find the intervals of concavity and inflection points of the function f(x) = x4 – 12x³ + 54x² – 1…

A: Given:      fx=x4-12x3+54x2-1   An Inflection point is a point on the graph at which the second…

Q: Q/ Find the root of the function by (Itration mathad) 2. Xo =o accu=o.0ol

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Q: 5x +2y -9z 44 -9x -2y +2z 11 6x +7y +3z =5

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Q: 3. Give an example of a function with discontinuities at x =1 and x = 5.

A: To Find : A function that has discontinuities at x=1 and x=5.

Q: If the equation of the tangent line to the graph of the function f(x) at the point (3,-6) is 2y + 5x…

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Q: Evaluate the limit. NOTE: Enter the exact answer. lim x→0 sin? 2x

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Q: dx 5. S- (4x – x2)°/2

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: てキ

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Q: Solve using the method of undetermined coefficients y'' - y' + 1/4 y=3 + e^x/2

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Q: Find the number of 3-permutations of a set with seven elements. a. 130 b. 120 c. 210 d. 100

A: Let's find.

Q: A quadratic function f is given. f(x) = x2 + 2x - 1 (a) Express f in standard form. f(x) =

A: f(x)=x2+2x-1a) Standard form of f is       f(x)=x2+2x+1-1-1f(x)=(x+1)2-2Therefore standard form…

Q: 5): If A is a n x n matrix such that A0 = In, then %3D A is a nonsingular matrix. Select one: True O…

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Q: The figure represents the quadratic f unction 1. Find the domain and range of the function 2. find…

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Q: The gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0).

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Q: if fcx) : gex) = X 11 X+ 1 find DE n Dg 2.

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Q: Find the minor M12 and cofactor A12 of matrix A. 1 6 A= 3 3-2 0 1 8. 5.

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Q: dy х+3у. dx 2х

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Q: The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is…

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Q: 1 let w = f(x, y, z) = Vx²y+y² z+z²x and x = 3st, y = 4st, z = 2st. a) Find ow dx dw b) Find dt and…

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Q: Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) 12 x in Quadrant II %D sin(2x)…

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Q: +2=0 (p) (e) In e -lna4 In 3 In r 4 In 3 (f) log16 Vr +1 = 4 %3D

A: In these equations x value exists only if the equation is valid.

Q: Choose the correct statement for the linear system whose augmented matrix is 1 -1 0 -3 8 -1 2 -2 3…

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Q: Evaluate the integral. 2. Se 3x dx 0.

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Q: 11. What is the best method is solvingſ sec'x dx? A) Integration by parts B) Reciprocal substitution…

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Q: Consider the following function. f(x) = -7x + 21x + 2 (a) Find the critical numbers of f. (Enter…

A: The given function,      fx=-7x3+21x+2

Q: Problem #8: Demand for a certain kind of SUV obeys the following equation, D(x, y) = 20,000 – V-…

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Q: 6) Find the resulting function after the following transformations are applied to the graph of h(x):…

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Q: 1. Prove using vectors that the points (4, 3, 0), (2, 0, 1), (4, 1, -1), and (2, 2, 2) are the…

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Q: Find f. f"(x) = 48x2 + 2x + 6, f(1) = 5, f'(1) = -4 %3D %3D f(x) = %3D

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Q: Solve the initial value problem. dy 2xy = 8x, у(0) — 0 dx y =

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Q: Find the power Series representation for the furiction and determine the radius of convergence.

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A: We will find minima, maxima or saddle point.

Q: 5. Mark each statement as true (T) or false (F). No justification is needed. Assume that converges…

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Q: Find the values of xER for which the function given below is both defined and continuous. f(x) = In…

A: f(x)=ln(x-9)Since f(x) is log functionIt is defined for all( x-9)>0⇒x>9