Consider the function f(x) = -2x³ + 36x² - 192x + 1.

Q: Jo sin(y²) dA, where D is the region bounded by D y = 2x, y = 2, x = 0. Evaluate

A: The D is the region is The figure of region D

Q: Let h(x) = 6x² +1+17x Determine the critical values of h. If multiple such values exist, enter the…

A: Given, .For find critical valuer put h'(x)=0.

Q: Find the area of the region that lies inside both curves. r = 5 + cos(0), r = 5 cos(0)

A: r=5+cos⁡(θ),r=5−cos⁡(θ)

Q: A particle moves according to a law of motion s = f(t), t≥ 0, where t is measured in seconds and s…

A: A particle moves according to a law of motion .where t is measured in seconds and s in feet.(e) To…

Q: f(0) = ln(cos 0) f(x) = log5 √√5x+1

A: f(θ)=ln⁡(cos⁡θ)

Q: Determine the function f satisfying the given conditions. f ''' (x) = 12 f '' (0) = 1 f ' (0) = 2 f…

A: Given that Let

Q: Find the critical numbers of g(x)=x√4x, x < 3. If th

A: g(x)=x4−x,

Q: nction f(x) = (2x-1, x ≤ 1 x², x>1 2 for all x. . tinuous and differentiable for all x. 2x for all…

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Q: p(x) = a + ax + a,x² + ... + 10x?

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Q: q(x)=−9x3 −9x2 −6x+6 Is the graph of q(x) concave up or down at the point with x-coordinate 1?

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Q: Given that f(x) = x³h(x) h(-1)=2 h'(-1)=5 Calculate f'(-1). -20 Hint: Use the product rule and the…

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Q: (a) Isolate h. V = { Tr² x

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Q: Prob #5 A Solve for angles A, B, and C in the triangle listed below. 17.8F+ C 35.2f+ 27.3ft B

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Q: Visually estimate the location of the centroid of the region shown. Then find the exact coordinates…

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Q: Differentiate. f(x) = In f'(x) = X 6

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Q: graph f(x - 4) - 5 below

A: given graph of f(x)graph f(x - 4) - 5

Q: If a 4th order linear differential equation is such that the corresponding characteristic equation…

A: If a 4th-order linear differential equation is such that the corresponding characteristic equation…

Q: Find the derivative. y=(x2+x)-3 OA. dy 3x5 (2-x³) dx (1+x³)3 OB. dy_3x4 (2-x³) (1+x³)3 dx 5C 31 ...

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Q: Find the following integrals using substitution. -1 1. fx sin xdx. 2. fcot x In (sin x) dx.

A: To find the following integrals by using substitution.

Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. √13n an =…

A: To determine whether the sequence  converge or diverge.To find the limit if the sequence is…

Q: Use the second derivative test to find the x-coordinates of all local minima given the following…

A: The given function is

Q: Given the function f(x) = -2x² Find the difference quotient Find f'(x) by determining lim h→0 -4…

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Q: f(x)=x54x

A: Given that functionWe have to find the derivative of the given function

Q: If an amount P is invested in the Mandelbrot Bond Fund and interest is compounded continuously at…

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Q: Use the properties of logarithms to expand the logarithmic expression. In (34) 94

A: By using the properties of logarithmic functions to expand the expression is     ln(x/94)

Q: 7.2x dy + y(2 + y²x) dx = 0

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Q: The velocity of a particle moving along a line is a function of time given by 79 t² + 12t + 27 v(t)…

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Q: Find a function y(x) such that 10yy and y(10) = 8. Y x

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Q: Simplify: x5/6y2/7x4/34/7 x2/3y1/7 Entry Tip: put the numerator and denominator in parenthesis. Also…

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Q: 2 p(x) = a₁ + ax + a²₂x² + ... + 10x⁹ = k = 1, 2, 3, ..., 9 •P(---) 10 1 k 00

A: It is a nine degree polynomial whose coefficient of x^9 is 10

Q: If the functions f, g are linearly independent, then the functions f − g, f + g are linearly…

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Q: Use the Table of Integrals in the back of your textbook to evaluate the integral: sec² (9t) tan²…

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Q: If 3x² + 2xy + y² = 2, then the value of dx -2 (b) 0 - at x = 1 is (c) 2 (d) 4 (e) not defined

A: The equation of the curve is The value of  at  can be obtained asNow, the point at which we need to…

Q: Solve e³t = 2000 for t. t≈ (Round to three decimal places as needed.)

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Q: Use the Table of Integrals in the back of your textbook to evaluate the integral: -xs -X sec (3x) +C…

A: Given Indefinite integral as follows

Q: y-values 9 8- 7 6 5- * 3 2 1 If f(x) f'(3) = g(x) 1 g(x) h(x) > 2 3 x-values then 4 y-values 4 3 2 1…

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Q: 1. Isolate X.8 (3 + x-4) 4 24+ T (3x + 1 8 = 3x + 1 2x-8 24-9 = X X = 15 T 8

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Q: List the four smallest elements of the set. (Enter your answers as a comma-separated list.) {y|y =…

A: {y|y = x2 − 3, x  integers}

Q: Find the derivative of the following functions using the quotient rule: You do not need to simplify.…

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Q: 1. 003 400 050

A: 2.

Q: Find the volume of the region under the surface z = xy² and above the area bounded by x = y² and x +…

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Q: Let f(x) = In(x). State if the following statement is true or false (a) The graph of f(x) has a…

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Q: Solve the following homogeneous diffe y"-4y'+4y= 0 »._4y"+л²y = 0, y(0) = 2, y'(0) = 0 x²y" - 2xy' +…

A: Given differential equationwhich is clearly a Euler Cauchy DE

Q: 5. (x + 2y + 3) dx + (3x + 9y − 5) dy = 0

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Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. 2-6n4 an =…

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Q: Use the sum and difference formulas to prove the following identities: 1. sin(x - 1) = sin x 2.…

A: 1.sin⁡(x−π)=−sin⁡x

Q: Solve for x. 3x = 22 Select the correct choice below and, if necessary, fill in the answer box to…

A: The given equation is

Q: Find the area of the region enclosed by one loop of the curve. r = 2 sin(90)

A: r=2sin⁡(9θ)

Q: 2. We found a solution y-sinx for the following differential equation. y"+y=0 a. Use Reduction of…

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Q: Plot the point whose polar coordinates are given. Then find the Cartesian coordinates of the point.…

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