Using horizontal rectangular elements, which of the following definite integrals give the volume of the solid obtained by revolving the shaded region about the y-axis? (0,5) (0.1) (2,5) 9-1²+1

Q: 16. If h(x) = f(2t +Vt) dt, find h'(-2).

A: If hx=∫0x32t+t3 dt, then to find h'-2.

Q: What is the value of the definite integral 8A 4 O 4T O -4T 8 √ √16 √16- x² dx?

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Q: Differentiate the function. V'(t) = V(t) = t-3/5 + +t²

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Q: Given f(x) = 13x³ + 18x² - 4x + 22

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Q: Consider statements I, II and III below on antiderivatives. I. If we know one antiderivative of a…

A: Explained below

Q: Find the derivative of the function. y = sin ¹(cos-¹(t))

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Q: Find the Taylor series (general form) of f(x): 1 X centered at x = 1.

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Q: uestion 1: For the graph of the circle below whose equation is of the form (x-h)²+(y-k)² = r2, enter…

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Q: The formula V = kr4 is used to predict how much the radius of a partially clogged artery has to be…

A: Given V = kr4where V = volume of fluid flow k = constant r = radius

Q: 15

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Q: Determine which graph corresponds to the area enclosed by the curves y= O O Find the area of the…

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Q: Suppose that so h(x) dx = Answer the following: A. Suppose that h is an even function. Evaluate…

A: Since you have asked multiple parts in a single request so we will be answering only first three…

Q: 31. dy If x³ - 2xy + 2y³ = 4 then, in terms of x and y, dx

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Q: Refer to the graph of y = f(a) with secant line PQ and tangent line PS. O PQ O PR O QR OQS OOO…

A: By the definition of dy  dy = f(x+ ∇ x) - f(x)

Q: 17. f(t) is the graph shown below and g(x) = f f(t)dt. Find g(0), g(1) and g(4). D 2 3

A: Let's find value of g(0),g(1) and g(4).

Q: Find the area of the given region. Use a graphing utility to verify your result. y = 1 + In x³ X y 1…

A: We can find the area of the region .

Q: In 1994, the moose population in a park was measured to be 4490. By 1999, the population was…

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Q: Evaluate the integral f(2x + by making the substitution u = x² + 3x + 8. 2x + 3) (x² + 3x + 8) ¹dx +…

A: Evaluate the integral. By making the substitution u= x2 + 3x + 8

Q: 13) y = [X²+2x-1'; dy = ? A) X+ Xt y B) 4y (x+1) (XH) (x²+2x-1) 3/2 D) - () ㅗ 2\x²2x-1

A: Question number 13 solved

Q: Evaluate the integral by making the given substitution. sec(52)tan (5x)dz, u = 5x + C

A: we know that   dxndx=nxn-1d(secx)dx=secxtanx

Q: What is d dx 7x 3x O 102 sin z √2 - sint dt? O-3√2-Sin 3z - 7√2 – sin 77 O 3√2-sin 3x - 7V2 — sin 72…

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Q: Given the graph below, solve the following inequality: k(t) < 0 +10 +RVEY 9 8 7 6 5 4 3 2 1…

A: To solve the given inequality

Q: 2) Consider the function: f(t) = 0, e-kt, 0 < t < 1 1 ≤t. A) Use the definition to find F(s) =…

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Q: Use the triangle to express 8 as a function of y. 10 08 = sin() 0 8 = sin n-¹(10) 0 0 = cos 1¹ (1)…

A: We can find the correct option in the below steps.

Q: Enter the equation of the parabola graphed below, using the vertex form y = a (x-h)² + k -5 -4 -3 -1

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Q: Question The Laplace transform of the function f(t)= e 2t+2t4 is L {f(t)} = Select one: O True O…

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Q: Show that the eigenvalues of A-¹ are ¹. 27 Show that A"x = λ"x if Ax = λx.

A: Given λ is an eigenvalue of A. So there exists a nonzero vector x such that Ax=λx....(i) 1.Since A…

Q: 3 x³e2x dx

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Q: a. Find the first four nonzero terms of the Taylor series for the given function centered at a. 13…

A: We will find the required.

Q: (b) n=1 3 2n-1

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Q: 3. Solve the following inequality: x³ + 2x²-3x x-4 ≤0

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Q: (d) Given the graph of f (x) below (blue), select the correct graph of the transformation y = f(x +…

A: To do transformation on given function f and determine its graph.

Q: F(s) = 9s² 2s - 3 12s + 20

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Q: x = The position of an object at time t is given by the parametric equations y = 5t² + 1 Find the…

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Q: d (sec-¹(2)) is equal to O O 1 2 √√4-1 1 In 2√4-1 O 1 √4¹-1 In 2 √4-1 In 2 2√4-1

A: Solution: ddxsec-1(2x) Apply the chain rule : df(u)dx=dfdu·dudx f=sec-1(u), u=2x =ddusec-1(u)ddx(2x)

Q: sin³ x + cos²x sinx = 2

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Q: The average cost per item to produce q items is given by a(g) 0.01g²-0.6q+17, for q>0. What is the…

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Q: For the function f(x) = 4 cotx determine its stretching factor and phase shift, and then graph it…

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Q: If G(x) is an antiderivative of f(x) = 2 + sinx and G(0) = -1-2, what is G(T)? O None of these. -3 3…

A: Given that Gx is an antiderivative of fx=2+sin x and G0=-1-2π. We have to find the value of Gπ.

Q: Identify the circle that has center (6,-3) and radius 3. Select the correct answer below: O (x+3)² +…

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Q: 8. The following table shows the number of Facebook members f(t) in millions over time t, where t =…

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Q: Find the partial fraction decomposition of 5 2 x²+x-6

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Q: (a) Find the velocity v (t) - |a| (b) Find the acceleration function. 71 sin (a) e7 [7 sin(81) + 8…

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Q: : You need to provide a clear and detailed solution for the following Questions: Question 1 Given…

A: Solution: Given data, y"-7y'+10y = -2e3t

Q: Which of the graphs below could be the graph of a power function with an even power? (a) ☐ (b) ☐ (c)…

A: Even power function With even-powered power functions, as the input increases or decreases without…

Q: 16) Sinx-cosy-2=0; dy = ? A) -cot X c) CosX siny B) -cot y d) -cscy cos X E) 2-COS X siny

A: given 16) sinx - cosy - 2 = 0

Q: ven the following equation of a circle in general form, find the equation in standard form by…

A: Given query is to find the standard form of circle.

Q: Graph the circle given below by moving the key points: (x - 2)² + (y + 2)² = 16 To graph the circle,…

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Q: 14. Given g(x) = f(t². + 6t16) dt, find intervals on increasing / decreasing and concave up/ concave…

A: The given integral function is: g(x)=∫-22x t2+6t-16 dt

Q: mpute the following integrals using suitable method. [xy dxdy, where R is theregion bounded by y=1,…

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