Given that f xdx = 1/2 and f²dx = compute the integral [*(1-x)²dx.

Q: Find the volume of the solid generated when the region ? bounded by the given curves is revolved…

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Q: Find the exact maximum and minimum volumes (in cm) of a rectangular box whose surface area is 1,300…

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Q: Let The coefficient of x' in the Maclaurin series for f(x) is: Answer f(x)=9e2x-x.

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Q: Determine the center-radius Form of the equation of the sphere whose diameter has endpoints at (2,…

A: The first question has been solved as per the request of the student.     The center radius form of…

Q: -x+1 3+z Given the points R (1, -1, -3), the vector v = and the line d: = 1 + y = 3 2 1. Determine…

A: Both questions are solved.

Q: 7. Show that the equation of the plane that has x-intercept a, y-intercept b, and z-intercept c…

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Q: 5. Suppose f is continuous on [2, 8]. Use the table of values of f to f(x) dx using a left, right,…

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Q: Find the general solution of the ff.differential equations.1.)dy/dx=x+1/2(y+3) 2.)dy/dx=y^2(1+e^x)

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Q: 23. Test the series below for convergence using the Ratio Test. Σ n2²n 8n-1 n=1 The limit of the…

A: Here we have, ∑n=1∞n22n8n-1

Q: 18. A radioactive substance decays exponentially: The mass at time is m (t) = m (0) ekt, where m(0)…

A: Concept: Mean life of a radioactive substance: The average life of all of the nuclei of a positive…

Q: Find the Area of the Surface obtained by rotating the curve about the y y = √√x, 1 ≤ y ≤2

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Q: Evaluate the following integrals. 13 1 sin²x -dx

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Q: Set up the double (dydx) and triple (dzdxdy) iterated integral that will solve the volume of the…

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bound by…

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Q: 5. Find the derivatives (a-b) and the limit (c): (2) ± √( 1 cos (1²) dt) (0) ² (154) dt dx 1 r2+x…

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Q: Find the volume of the largest right circular cone that can be incribed in a sphere of radius 3. 3 y…

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Q: 43. Evaluate: S(2ex - 4x) dx A. 2e*4* + C B. -2ex + 4x + C 4x C. 2ex + C In 4 4x D. 2e* + + C In 4…

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Q: Please answer both

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Q: For each of the following, state whether it has meaning. If not, explain why: (a) (ū. v) — |w| (b)…

A: We have to find the vector meaningfull

Q: Determine the value of x when the slope is its maximum for the function f(x)=2cos(3x)

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Q: If sin 20 = √3, 0≤ 20 ≤ 2π, calculate the values of

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Q: If f(x) = 2x + 1 and g(x) = ln(5x − 2) then (f. g)'() = A. None of these B. 1.25 c. -0.386 D. 20

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Q: 112 points/ Use algebraic techniques to determine whether the following function is even, odd, or…

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Q: 2. Verify using the principle of Superposition that y₁ = ²* and y₂ = e* are solutions of y" - 7y'…

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Q: Let C be the parametric curve defined by Ja(t)=1²-t-6, [y(t) = 41³ + 3t² - 6t. Determine the point/s…

A: a) Given that: xt=t2-t-6yt=4t3+3t2-6t For a horizontal tangent line, the slope must be 0. That…

Q: Find the derivative of f(x) = ✔ (6x¹ + x² − 1) 5.

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Q: x2 (x+2)³ dx In Ix + 2) + 4x+6 (x+2)² +C In Ix + 21 4x+6 (x+2) +C

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Q: Calculate the average rate of change for the function f(x) over the interval-1≤x≤3

A: Topic = Algebra

Q: A payment of $2,690 was due two years ago, and a payment of $1,650 is due today. What single payment…

A: We have to solve for single payment.

Q: Determine the x- and y-intercepts for the given function. B(x)=5x+8

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Q: 4. Determine the number of terms in the sequence: -45, -32, -19, -6, 410 ***

A: There are 36 terms  in the sequence.

Q: ind g'(3) given that f(3) = -1 and f'(3) = 5. (a) g(x) = 2r³-7xf(x)

A: Topic:- application of derivatives

Q: 2 is: The slope of the tangent line to the curve y = - at the point 3, x The equation of this…

A: We have to find out the slope

Q: Find the orthogonal trajectories of the given family of curves. 1. y = c (sec x + tan x )

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Q: 9 Determine the area to the right of g (y) = y² +4y-5 and to the left of the y-axis.

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Q: 2 J xe9x da 0

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: Find the volume generated by revolving the area bounded by y² - 4y - 4x + 4 = 0 and x = 1 about the…

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Q: 18

A: We will solve the problem

Q: Evaluate the y' and Simplify the answers I Direct trigo functions y = x² sinx + 2xcosx - 2sinx

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Q: Find the particular solution of dy/dx=6e^3x+1,andf(0)=0.

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Q: 3. z = x+y x-y

A: The given function is  z=(x+y)/(x-y).

Q: 3. Let 7 and w be vectors such that v=(2, 2, -1), |||| = √2, vw=-3, and × = (2,-1, 2). a. If u =…

A: Key points: We say that 2 vectors are orthogonal if they are perpendicular to each other. If two…

Q: Evaluation. Determine the antiderivative for each. Show complete solution 1. S dx 5x³-3 √x3 2.…

A: As we know that; The Sum Rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1       1).…

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bound by…

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Q: Consider the point P (-3,-1,5), the line : x = 3 t. y, y = -6t -3₁ z = 2t +1, and the Flane 1² : 7…

A: Given

Q: TYPEWRITTEN

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Q: A company determines that its total cost, in thousands of rands, for producing x  items is (image…

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Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. 1 S₁° 19 dx…

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Q: 3. Find a vector equation of the line that... a) passes through (-3,5,-2) and (7,-3,1) b) has…

A: vector equation of line

Q: 11. Evaluate 1 (a) √x (x² +1)³dx, (b) fdx (c) fda (d) fx x+2 ev dx √x²+4x IT'

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