= A rectangle is inscribed with its base on the x axis and its upper corners on the parabola y -4x² + 12x. Find the dimensions of the rectangle with the greatest possible area.

Q: Evaluate the function f(x)= -2x+8 at the indicated values. a) Find f(3). b) Find f(-2).

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Q: x-2 3. lim x-2x²-4

A: Here we have to find the limit of the function.

Q: S Find the derivative of the following functions. Use long method. a. f(x) = 3x² + 5x - 100 f(x) =…

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Q: Evaluate [ (cos² 0 + 2 csc² 0 + sin² 0) do .

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Q: Find all values of m so that the function yemx is a solution of the given differential equation.…

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Q: What is the largest rectangular area that can be enclosed by 100 ft of fencing. (Non-anonymous…

A: Given problem:- What is the largest rectangular area that can be enclosed by 100 ft of fencing.

Q: Which of the following gives the volume of the solid obtained by rotating the region R about the…

A: We know that the area of the curve y=f(x) , the X axis and the lines x=a ,x=b is revolving about the…

Q: Question 10 of 10 Find the general term of the sequence, starting with n = 1. Determine whether the…

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Q: Compute Au, where A Au = = 1 (56) 4 and u= (9).

A: The simple matrix product..

Q: Verify that Rolle's Theorem can be applied to the function f(x) = x³ - 8x² +17x - 10 on the interval…

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Q: Quadrilateral MATH is shown. LO 5- 4 -3- 2- M A -5-4-32-10 1 2 3 4 5 -1 T H -5- Quadrilateral MATH…

A: Given data :- M(-1,1) , A(1,1) ,T(2,-2) , H(-4,-3)  Dilation with scale factor of 2.5 Center of…

Q: The graph of f(z) is given below. Which of the following statements about f(z) are not true? Note:…

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Q: Identify the open interval on which the function is increasing or decreasing. h(x) cos(쯤), 0 < x <…

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Q: Use the Laplace transform to solve the given initial-value problem. y'' − y' = et cos t,    y(0) =…

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Q: Let f a continuous function in [0,1], an integral equivalent to π/2 f (cos(x)) sen (x) dx 0 after…

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Q: If w = cos(xyz), compute for O-x²yz cos(xyz) - x sin(xyz) -x²yz cos(xyz) + x sin(xyz) O x²yz…

A: This question can be solved using the concept of partial derivatives.

Q: Find f'(x) if f(x) = = f(x) = x² 3x-2'

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Q: Solve the differential equation (24xy + 40y²) + (8x² + 40xy)y' = using the integrating factor µ(x,…

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Q: d dx [x² tan x] d sin x dx [1 + cos x] ₁ || 1 1 + cos x

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Q: 3. log (x²+x)-log.(x-1)-2 А. 2 Oi J. оо о で В. 16 C..X D. - 16 -

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

Q: al fraction decomposition of the rational proper fra P(x) A B + x+1 x-3 at's the value for A and B?…

A: We have to choose the correct option from the given options according to the given information

Q: Consider the following system of linear equations: -11x + 3y +-31z 118 -4x + 1y+-11z = 42

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Q: S dt e2t 6-2e²t

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Q: Evaluate the definite integral. TT/3 [C [(sec t tan t)i + (tan t)j + (2 sin t cos t)k] dt 10

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Q: (3 - x) dx is equal to ° S (3 − x) dx + ["' (3 + x) dx °₁ (3 - x) dx ° L₁ (3+2)dz + f (3-2) x) dx x)…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 1.tr Y= 4 In ( In (In(sec(x)) then Y 14 (lan)! In ((In (sec)) In (sex);| O True O False

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Q: Figure #2 a: I in b: 2.5in C:2.5in Figure #3

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Q: he "Garbage Project" at the University of Arizona reports that the amount of paper discarded by…

A: We use a standard normal table to find the value  Given mean=9.4 standard deviation=4.2

Q: Solve the given differential equation. All solutions should be fou dy x6 - 2y dx X NOTE: Use c for…

A: We have to find out solutions

Q: Given the piecewise function below, find the value of k which makes the function continuous. f(x) =…

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Q: B/ Find the value of lim,-.. 1. ²/2 O 1 O 2 7x²+x-100 2x²-5x N NIN

A: To evaluate: limx→∞7x2+x-1002x2-5x

Q: Q2/ Examine the following surface for maximum, minimum, and saddle points 2 = x² + y² + xy + 4x - 4y…

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Q: Determine whether the differential equation (7x+8) + (7y - 7)y' = 0 is exact. If it is exact, find…

A: To determine that the differential equation is exact or not.

Q: 2. ) Consider the surface x² + y²-2xy-x+3y-z=-4 at the point Po(2, -3, 18). Determine the following:…

A: To find the tangent and normal.

Q: hand-tossed pizza base starts off as a ball of dough with a volume of 400π cm3 . First, the cook…

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Q: Find the general solution of the given differential equation. y’’+2y’-8y=0 topic: complex roots of…

A: Explanation of the answer is as follows

Q: a. Show that f has a removable discontinuity at x = 3. f(x) = x²7x+12 x + 2 x = 3

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Q: 3x + 5, 13+¹6, Find a value of x, if any, at which f(x) = If f(x) is continuous for all values of x,…

A: Given: Notice that 3x+5 is continuous for x&lt;4 and 13+16/x is continuous for x&gt;4. Now, we need…

Q: Graph the following function. Show at least two cycles. Use the graph to determine the domain and…

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Q: Find the equation for the tangent line of the graph of 4 y = x² at (-2, 16). Equation:

A: Here we have to find the equation of the tangent line of the graph y=x4 at (-2, 16)

Q: (3 − |x|)dr is equal to L (3 (a) f( (3 - x) dx (b) [(3+z)dz (c) [²₁ (3 - x) dx + [² (3 + x) dx (d)…

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Q: et J ((et + 4)²-9)³/2 9)³3/2 dt.

A: See the details solution in below

Q: Solve the given differential equations: X 2. y' = , y(0) = -2 y+x²y

A: To solve the given differential equation.y'=xy+x2y, y0=-2

Q: Matrices A and B below are row equivalent. For each of the concepts following, choose (check) one…

A: See the answer below

Q: Find the exact value of each of the remaining trigonometric functions of 0. cos 0 = - 4 5 0 in…

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Q: y = x4 - 8x² + 8

A: Here we have to sketch the function y=x4-8x2+8 ............................................ (1)…

Q: Let f and g continuous functions in R that satisfy at the same time all the following equalities :…

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Q: 36. Which one of the following is true for all z ER? (a) z sin(2) dx = (1-2) cos(x) + C (c) (b)…

A: Now that we know that the integral of x sin x is equal to −x cos x + sin x + C, we will derive this…

Q: Consider the function f(x) = (3x² − 4)(x² + 6). (a) Compute the derivative of f(x) by multiplying…

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Q: Consider the following statements: I. 27x+3, 27x11, and 27x + 17 are antiderivatives of 27. II. In…

A: Given : 1. 27x+3, 27x-11 and 27x+17 are antiderivatives of 272. In general, 27x+C is an…