Find the area of the region bounded by the graph of f(x) = x(x - 3)(x + 1) and the x-axis on the interval [- 1,3]. The area is (Simplify your answer.)

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Q: Find all points where the function is discontinuous. 5)

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Q: Answer the following questions for the function f(x) = a/a² + 9 defined on the interval – 6 <a < 7.…

A: According to the guidelines, I am answering the first three subparts. Please repost the remaining.…

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A: The function id concave downward if f''(x)&lt;0

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A: Initial velocity of the hammer, u = 0 m/s Vertical distance above the surface of the moon from which…

Q: 3. Prove: a) Bo(U,4,)=U,(BO4) b) BU(N,4)=N,(BU4)

A: a) B∩∪iAi=∪iB∩Aib) B∪∩iAi=∩iB∪Ai

Q: 58. Particle Motion The position of a particle as it moves along a line is given by s(t) = – 12r +…

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Q: Consider the function f(x) = 3x + 6 For this function there are two important intervals: ( – 0, A)…

A: The given function,      fx=3x+64x+2

Q: 1) Ifféx) =x + 5 and g(x) = x² -3, then find g(Ư(0) . 2) Iffés) = secx, and g(x) = L, then find…

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Q: x2 +x+1 dx 2x2 +2+x³+x

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Q: Let f(x) be the function 1 Then the quotient x + 8 f(5+ h) - f(5) -1 can be simplified to h for: ah…

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Q: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =…

A: Given function F(x,y)=( 2x-6y ) i+(-6x+14y-7) j

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Q: Evaluate the line integral, where Cis the given curve. (x + 6y) dx + x² dy y (6, 1) C (7, 0)

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Q: 1 In solving the antiderivative of f(x) = 2- sin(x) by miscellaneous substitution, the substitution…

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Q: S tan³ 6x sec10 6x dx 1 sec1²6x + sec1º6x + C 72 1 60 B none of the choices 1 -sec1²6x + 72 1 1…

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Q: Prove the identity. 1 + tanh(x) – e2x 1 - tanh(x) 1 + cosh(x) 1 + tanh(x) 1- tanh(x) 1 - cosh(x)…

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Q: S sin®xdx

A: ∫sin6x dx       We have sin2 x=1-cos2x2 Then ∫sin6x dx=∫sin2 x3dx                  =∫1-cos 2x23dx…

Q: Find the derivative. (The Fundamental Theorem of Calculus -- Part 1) 19) y = cos ft dt COS-

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Q: Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints…

A: Solving

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Q: 3. Find dy/dx x = Vy + Vỹ 1 + Vx 4. Find the second and third derivative of y = 5. Find dy/dx y =…

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Q: Find the indefinite integral. (Use C for the constant of integration.) sinh(5 – 2x) dx

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Q: Evaluate the following limits: V10 + 6х — 2 (a) lim x→-1 x2 – 2x – 3 1 – sin(x) (b) lim x→5 (2x –…

A: Use l hospital rule for finding the limit.

Q: Find the integral. Box Final Answe r. For the definite integral, gve the exact answer only Ssin(Bx)…

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Q: Evaluate the definite integral. NOTE: Enter the ecact answer. 13 ti+t°j dt

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Q: For the following integral, answer the questions below. ets dx (a) What should be your first step in…

A: Use first substitution then use integration by part

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A: Explanation of the answer is as follows

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A: I am attaching image so that you understand each and every step.

Q: 31. Jul = 9.0 = 335°

A: Given query is to find the component of the the vector.

Q: 1 In solving the antiderivative of f(x) = by miscellaneous substitution, the substitution z =tan|…

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Q: (1 + Зx) dx

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