Find the average value of the function f(x)=x²-9 on [0,3]. The average value of the function f(x)=x²-9 on [0,3] is

Q: Find the differential equation such that y(x) = c₁(x-4)³ + c₂ln(x-4) (x-4)² 64x²d²y + 2 +60x+y=0 dx²…

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Q: The position function of a particle is given, in metres, as s(t)=t 4-10t 3+36t 2+10t+12 where t ≥0…

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Q: simplify 12cos4xsin4x

A: Simplify 12 cos(4x) sin(4x)

Q: J = [sen² (4) cos² (4)dy. When applying variable change u= cos , J is equivalent to: O a) fu² (1-²)…

A: Given,       u=cosφ     du=-sinφdφ -du=sinφdφ

Q: 2. Show that the function. 5x²³²Bin 12 F(x)= โ x2 0 (x=0) is not of bounded variation on [1,1].…

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Q: Suppose that the marginal revenue from the sale of x units of a product is MR = R'(x) = 3e0.01x.…

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Q: 4) Find equations for the planes: b. The plane through (1.–1,3) parallel to the plane 3x+y+z=7

A: Given problem:- Find equations for the planes:   b. The plane through (1.-1,3) parallel to the plane…

Q: Y=t-2√√√x + X Find domin and ringe

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Q: 11

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Q: B2. Find the integrating factor by inspection then solve.  y(y2 + 1)dx + x(y2 - 1)dy = 0

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Q: Psychologist L. L. Thurstone suggested the following relationship between learning time T and the…

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Q: √√3 Lett be a real number and let P (1/1-4/3) 2 2 (a) Find the values of cost, and tant, and then…

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Q: Effect of Housing on Start Jobs The president of a major housing construction firm claims that the…

A: This question is related to rate of change, we will solve it using given information.

Q: Using the technique of substitution with u = -t, the 01 / 2²1-41 des du 70 1 04/2² du ㅠ O -1 za 2²…

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Q: an integral corresponding to the area of the region bounded by the curves of the functions f and g…

A: f(x) =x2 -4x  g(x) = -x2 here area function = f(x) - g(x) = x2 -4x  -(-x2 ) = 2x2 - 4x

Q: The population of a small country by year is shown in the table below. Year 1955 1960 Population…

A: If population of a city x in 1950 and y in 1960 then absolute change of population=(y-x)  As per our…

Q: Q2] (A) Find the general solution to ONLY ONE of the following differential Mations (1) (sec(y))2…

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Q: 3. (3y² + xcos xy) + (3x² + ycos xy) = 0 dx a) y + sen xy + x³ = 0 y² + sen xy + x³ = 0 y² + sen y +…

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Q: 4) Find the intervals where the following function is concave down: ππι y = 2sin² (2x) - 4x, x € -

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Q: The projected population of a certain ethnic group(in millions) can be approximated by p(t) =…

A: Solve the following

Q: Given x³ + xy - 4x = 4: dy (a) Find by differentiating implicitly. Do not substitute for y. dx dy dx…

A: Explanation of the answer is as follows

Q: Suppose that f and g are functions that are differentiable at x = 1 and that f(1) = 4, f'(1) = -3,…

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Q: Curve Sketching Week #14 Sketch the graphs of the following functions. Pertinent aspects of the…

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Q: Find the limit. Enter the exact answer. If the limit does not exist, indicate that using the check…

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Q: Find the directions of maximum and minimum change of fat the given point, and the values of the…

A: Given:      fx,y=9y2e6x The gradient of a function z=Fx,y is denoted by ∇Fx,y The direction of the…

Q: When applying substitution (u=tan(x)) to [s sec¹(x) tan(x) dx is equivalent O a) [ (u³ + u) du O b)…

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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: Factor the trinomial. 6q²-25qt+14t² Select the correct choice below and, if necessary, fill in the…

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Q: kx 4+x² If k 1, evaluate k (a) 2 kx (b) 2 J₁ arctan (2x) + C arctan (2x) + C dx. (c) // ln(x² + 4) +…

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Q: foxdx

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Q: 8. Find the length of the curve r(t) = from t = 1 tot = 5. 9. Find the curvature of the curve r(t)…

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Q: f (Ina) ² da 2

A: This question is based on integration by parts.

Q: Question 4 A student club is selling t-shirts for Thon every weekend. They found that when selling…

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Q: te the function for the given values of 3) [-2x+5, for x < -1 f(x)=x²-4, for-1 ≤x<3 for x ≥3 12, (a)…

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Q: 1 If f(x) has an inverse function f-¹(x), could either the graph of for the graph of f-¹ be…

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Q: Verify that the indicated function is an explicit solution of the given differential equation.…

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Q: 2. Find y' if y = 7* (log4 x)⁹.

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Q: If y = ecos(x) then y" + sin(x) y' cos(x)= ***

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Q: If G is an antiderivative of the function g, so the following integral is equal to what option? 1-26…

A: Given problem:-

Q: Describe the transformation that can be applied to the parent function g(x) = e to obtain the graph…

A: Explanation of the answer is as follows

Q: Find when y = cos(sin 2x). ay dx dy dx

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Q: 3. Given u =(3, 10,-8) and v = (-1,6,4), a) find 3v--u

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Q: -32 1 ย X

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Q: Exercise 2.5, Problem 26 a. Show that f has a removable discontinuity at x = 3. / f(x) = x² - 7x +…

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Q: For the function f(x) = 2x³-5x² +11x +3, find f''(x). Then find f''(0) and f''(2). To find f''(x),…

A: The given function is f(x)=2x3-5x2+11x+3

Q: OR Find the complex Fourier transform of the convolution of f(x)= [3, -1<x<1 0, elsewhere, g(x)= X,…

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Q: Do not use calculators. Approximated decimals are not accepted. Let j=8 k= 3 Solve the equation:…

A: To solve: The equation log3x-9+k=2-log3x-1+k. Given: The value of k=3 Concept used;…

Q: x²-3x - 10 f(x) = x+6 [-2,5] Yes, Rolle's Theorem can be applied. No, because f is not continuous on…

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Q: d dx [47 tot 1 3x17 5 13 + 10 L 25 +100

A: This is a problem related to derivative of the function. Based on the general formula and concept we…

Q: A. Solve the following 1st order differential equation: dy (4 y + cos y). - 3x² = ( 0 dx B. Solve…

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