Using the cylindrical shell method, determine the volume generated by revolving about the y-axis, the region defined by the curves. Draw the region and a representative shell

Q: B. Find all the rational zeros of each 28. 2x³ +9x² + 7x-6=0 29. 2x³ + 16x² + 14x = 0

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Q: Find the limit. sin (0) lim 0 0 30+ tan (0)

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Q: Find the derivative of the function. 4x - x² f'(x) = f(x) = 1 x² - 5

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Q: x³ + x² + 2x + 1 - dx (x² + 1)(x² + 2)

A: take partial fraction

Q: x +4 x² + 2x + 5 -dx

A: To calculate the integral ∫x+4x2+2x+5dx.   Use the common integrals:…

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A: Solution: From the given graph pattern we can observe that it is cotbx function

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Q: The position of a car being driven on a straight road is given by s(t) +3)³/2 as measured in feet…

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Q: (2) Determine what comes next in the given pattern and provide solution/explanation 12, 5, 24, 10,…

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Q: 2 Find an equation of the tangent line to y = f(x)=√x +55 at x = 3. Enter an exact numbers, do not…

A: To find an equation of the tangent line to y=fx=x2+55 at x=3.

Q: et H(x)=F(G(x)) and J(x)=F(x)/G(x). Suppose F(8)=9, F′(8)=1 G(8)=2, G′(8)=3 G(10)=8, G′(10)=−6 then…

A: The given data is: Hx=FGxJx=FxGx    F8=9, F'8=1G8=2, G'8=3G10=8, G'10=-6

Q: 5: Choose the correct answer for the following questions: The figure bellow shows the graph of a…

A: Given graph:-

Q: A. Find d/dx(5^xln(x+8)) Answer:

A: 1) Given:     ddx5xlnx+8      Apply product rule:        f·g'=f'·g+f·g'…

Q: Find an equation of the tangent line to the Curve x² + xy-y²-1=0° at the point. (1, 1)

A: Given query is to find the equation of the tangent.

Q: B- If the function is continuous at x = 3 find k value: (k f(x) = { xª − 81 - x - 3 x = 3 x = 3

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Q: c) Find the area enclosed between the curve y = cos² x and the line y = 1: of y = 1 Ele y = cos².r

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. 8 Σ(−1)k+1 k=1…

A: ∑k=1∞ -1k+1k+6kk+7

Q: Round your final answer to four decimal places. Use linear approximation to estimate the quantity…

A: We knowLinear approximation  for the function f(x) at x=a is Lx≈fa+f'ax-a            ............(1)

Q: Use the graph of the function f to decide whether the value of the given quantity exists. (If an…

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Q: Find the absolute maximum and minimum of the function on the given domain. f(x,y) = 6x² + 7y² on the…

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Q: ex f(x,y) = (4x-X ахду d³f dx dy d x 3 of dx²dy mark X8 t C

A: Given:   f(x,y) = (4x - y)7

Q: 4x 2 x³ 3 - x²-x+1 S dx.

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Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = xo and then find the nth…

A: The function is given by fx = ex To evaluate: The Taylor polynomials of the order n = 0, 1, 2, 3 and…

Q: The price-demand and cost functions for the production of microwaves are given as ?=240−(?/40) and…

A: We need to solve cost problem.

Q: (2) lf g(x) = cos(2x) then evaluateg'(0). Use this value and find the π equation of the tangent line…

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Q: find the differential equation for following family of curves. Question: 1. circle whose center at…

A: Topic = Differential equation

Q: / x² (x + 1)³° dx

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Q: J - 10 -dx (x − 1)(x² + 9)

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Q: Find the solution of the given initial value problem. ty' + 2y = sint, y() = 7, t > 0 సా ||

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Q: v(x)u'(x) then h(x) = u(x))~ u(x) + (In (u(x))v'(x)) thenh(x)= u(x)" Use the above definition to…

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Q: Graph 4x-y=-8. -20 -18 -16-14-12-10-8 --6 20- -81 14- . 10- 84 -9 4 ++ ---6- -8- -10- -12- -14- -16-…

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Q: The graph shows the depth of water W in a reservoir over a one-year period as a function of the…

A: Given Graph:-

Q: Use technology to solve the system of equations. Express all solutions as decimals, rounded to one…

A: Given

Q: If x²y + y²x = 6, then find y' at x = 2.

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Q: 6. Find dy dx of cos y - 2xy + 3x = 2x sin x

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Q: evaluate  lim x → 0− e7/x. If we let  t = 7/x   we know that  t → −∞  as  x → 0−.  Therefore, by…

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Q: Evaluate the integral. (sec²(t) i + t(t² + 1)8 j + t7 In(t) k) dt + C

A: to evaluate the integral

Q: Find the area of the surface generated by revolving the curve y = 0≤x≤2, about the x-axis. 9 1 The…

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Q: Find the cross product a x b. a = ti + cos(t)j + sin(t)k, b = i sin(t)j + cos(t)k Verify that it is…

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Q: Find an equation of the tangent plane to the given surface at the specified point z = 4x² + y² - 9y,…

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Q: Sketch the curve with the given vector equation by finding the following points. r(t) = (t, 3 t, 2t)…

A: Given : r(t) = { t, 3 - t, 2t}

Q: 5 - [y√y-1) - 1) dy

A: Note: Since, the student has not mentioned question number clearly, but this is a standard question,…

Q: Find the points at which the following polar curve has a horizontal or a vertical tangent line.…

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Q: Evaluate the indefinite integral Sin(x) dx

A: We need to solve the following indefinite integral ∫lnxdx Formula Used: The integral can be solved…

Q: 1. ſ X (2x-5)² (3-4x) dx.

A: Solution: ∫x(2x-5)2(3-4x)dx Take the partial fraction ∫398(2x-5)-514(2x-5)2-349(4x-3)dx

Q: Find the slope of the tangent line at the point (1, 1) to the curve having equation 8x²+2xy-8y² =2

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Q: Find the derivative of P = t^6 ln(t+1)

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Q: 2. Find the derivatives of the following functions. (a) y=x²ln (x+9) (b) y = x +4x² log₂ (x) (c) y =…

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Q: Complete the ordered triple. 7x y + z 4x + 2y3z x - 3y + 2z - 33 47 16

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