Find the average value of f(x) = x² on the interval [2, 4]. Answer:

Q: Evaluate: [x(1-2²) da ¾ O ³(1-x²) + C 3 0-² (1-x²) O 3 + C O 2/(1-x²) + C 3 O ㅇ글 (1-22) : + C (1-x²)…

A: Here we have to find the integral.

Q: 1 1² +49 When solving O a) I = [sen (0) de Ob) I=tan(0)de O c) I = cos(0)de I= O d) I-sec(0)de I=…

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Q: (5) f(x) = cos (5 - 2x) (7) f(x): = cos (√x³ + 1) (9) f(x) = cot (x5) (6) f(x) = cos (4x7 + 3) (8)…

A: as per company guidelines we solve only first three subparts when multiple parts question being…

Q: Use the method of reduction of order to find a second solution of the differential equation ty" +…

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Q: Determine dy/dx of = 3x(sin(2/2)) O None of the choices O 12/cos (2/2) + sin(2/2) 0-12 sin(22) + 3…

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Q: Question 6 Given: f (x, y, z) = cos(xyz) + ln x5 - sinh y² + 3z Find: af(x, y, z) дz at P(-1, 3, 0)…

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Q: 5. Integral ReR dR

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Q: In a circumference of radius r (in meters), its radius increases at a rate of 2.8 meters per hour.…

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Q: Let [ f(x) dx = 5, -6 Find and -3 [ f(x) dx = -4.5 -4.5 -3 6 (5 f(x) - 6) dx = f(x) dx = 6, f(x) dx…

A: The given integrals are;  f(x) , limit from -6 to -1.5. f(x), limit from -6 to -4.5. f(x), limit…

Q: ४ = (y3/2/3) - y¹/2 from y = 1 to y = 9

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Q: 11. Find the angle between the planes: 4y + 3z = -12 and 3x +2y + 6z = 6.

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Q: this is incorrect please resvole

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Q: B)Convert r = √2 cos (0-) to cartesian.

A: we need to convert polar coordinate into cartesian.

Q: Find the value of E, the margin of error, for c = 0.99, n = 15 and s=5.4. OA. 1.072 OB. 3.659 O C.…

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Q: 10. Integral 2-t dt

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Q: If f³ f (x) dx = 6 and ſ ƒ(x)dx = 4, then ſ5 (3 + 2ƒ(x))dx : = 35 10 23 20

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Q: 9. Integral (2x-5) ai x² = 5x + 3 -

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Q: Find area bounded by y=0,y=√x-x² using double integration.

A: To find the area of the given region.

Q: In the attached figure are represented the continuous functions g: R → R and h: R → R 9 h If it is…

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Q: Given the functions: f(x) = 7x g(x) = x+2/ h(x) Evaluate the function (g-h)(-4) for the given value…

A: Given :fx=7xgx=x+2hx=1x+5

Q: Solve using Inverse Operaators. y"" - y = 4e-x + 3e2x; Particular Solution: Y=C1+ C₂ eax + C3 ebx…

A: Given that,

Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 4…

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Q: Find dy given that x = sec² y y. dx Osec² ytan y cos² y tan y 2 Osin² y cot y O cos² y cot y

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Q: o what does it con s conditionally conv 1. onvergence for at is the radius of approximation of e √2,

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Q: A fast-food restaurant has a cost of production C(x) = 14x + 126 and a revenue function R(x) = 8x.…

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Q: If f(x) dx = 3 and g(x)dx = −2, then which of the following must be true? I. f(x) > g(x) for all a ≤…

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Q: B)Solve the differential equation da x+4y

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Q: QUESTION 5 Given function f(x,y)= A. 2 B. 3 C. D. 0 ANSWER: 6 2 63xy of Evaluate at point (0, 1). ox

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Q: Find the general solution of the differential equation y" — 4y' + 104y = 0. NOTE: Use c₁ and ce as…

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Q: Classroom activity 9.1 the monthly income earned by each of the following workers paid by the hour…

A: We have to determine the monthly income.

Q: ror(4)). 95. Find the restrictions in the domain, if any, for If there is more than one restriction,…

A: Note: The first question that is question 90 seems incomplete. So, solving 95 for you.

Q: If f f(x) dx = 3 and I. III. [f(x)g (x)] dx = −6 III only I, II and III I only O II only g(x)dx =…

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Q: B. Given that f(x) = {(-2,1), (1,4), (2,5), (3,6)} g(x) = 6 + 4x h(x) = -x² + 2 find

A: given

Q: Suppose that the total profit function for a company is given by P(x) = 4x³ - 210x² + 3600x - 200,…

A: We have to choose correct option for given questions.

Q: Solve the initial-value problem. x(t) = x" + 3x' + 2x = 1 + t², x(0) = 0, x'(0) = 2

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Q: Evaluate the integral using integration by parts. Scot-¹(8y)dy 1 Scot ¹(8y)dy = -x In (cos (6y)) + C

A: The given integral,       ∫cot-18ydy

Q: 10. Determine the point on the line x + 2y = 2 that is closest to (0, 0). Draw a sketch.

A: point which is closest to origin

Q: ди 2²u Consider the heat equation = +2x, for a bar of length L=1, with non homogeneous boundary…

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Q: Refer to functions s and t. Find the indicated function and write the domain in interval notation.…

A: Given sx=x-3x2-36 and tx=x-63-xWe need to find stx and its domain.

Q: 7. Integral cos x dx sin x

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

Q: a. Use limits to find the derivative function f′ for the function f. b. Evaluate f′(a) for the given…

A: The given function,    fs=5s3+3s, a=-3

Q: Use the Inverse Function Theorem to find (h-¹)' (7) given that h(x)=√10x + 9. Note that h(4) = 7.…

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Q: dy -(x²+y) B)Solve differential equation = dx x+siny

A: Here we have to solve the differential equation.

Q: Calculate the future value of end- of-month payments of $500 made for 4 years into an investment…

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Q: The curves y = In x and y = 3x² have parallel tangent lines at x = A) ± √/ B) C) √6 E) 2

A: Two lines have parallel tangent if slop at the point is same.

Q: X f(x) g(x) -2 5 1 -1 2 3 0 4 1 -2 2 -4 -3 -6 -1 f'(x) -4 -2 1 5 -5 g'(x) -1 3 -3 4 2

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Q: Find the unit tangent vector T(7) for the line tangent to the space curve r(t) = (12 cost, 12 sint,…

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Q: Solve the initial value problem y″ + y = 0, y(7) = 8, y′(π/3) = − 16 y(t) = √√3cost + 8√√/3sint y(t)…

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Q: Evaluate x+1 S ex x² dx O e.e= + C O-e e + C O e e + C e = + C O

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Q: Complete the table for the equation y=x-2, and graph the equation. X -2 - 1 0 1 2 Use the graphing…

A: line