Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis. y = 2-x 2.5 1.5 y 14 0.5 0 0.5 1 1.5 2.5

Q: Find the area of the region enclosed by the curves x = 1 - y² and x = y² – 1. Make sure you label…

A: To find the area of the region enclosed by the curves x=1-y2  and x=y2-1.

Q: A force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is attached to the end of…

A: FOrce act  upon the spring  F= 640 N The  distance stretch by the   force  x  =4 mby  spring  force…

Q: A steady wind blows a kite due west. The kite's height above ground from horizontal position x = 0…

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Q: The equations given below illustrate a suspected number pattern. Determine the next equation. 1=1²…

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A: Graph of the function is given, we have to find the given limits.

Q: The region bounded by the given curves is rotated about the specified axis. Find the volume of the…

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Q: The rate of change, de, of the number of people entering a movie theater is modeled by a logistic…

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Q: Consider the function h(x), for which h(2) = − 1 and h'(2) = -6. Find f'(2) for the function f(x):…

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Q: reasons for your answers. 1 to be continuous at x = 1 or -1? Give

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Q: Sorry I can't see the solution it's too messy, could you please write the answer part again please

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Q: Consider the following function. f(x) = (x-8)2/3 Find the derivative of the function. f'(x) = X= 2…

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Q: End Behavior of a Po Identify the End Behaviors for the function graphed to the Right hand end…

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Q: Determine whether each integral is convergent or divergent. Evaluate those that are convergent. Lo…

A: To determine whether each of the following integral is convergent or divergent. To evaluate those…

Q: the following graph. -8-7 -6 -5 -4 -3 -2 4 3 Identify the vertex of the parabola: Remember that the…

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Q: For the parabola graphed below, identify its vertex, axis of symmetry, and state if it opens upwards…

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Q: -1 (A) (B) (C) (D) (E) 3 2 1 -1 -2 1 Using the graph above, evaluate the following limit. lim f(x)…

A: Explanation of the answer is as follows

Q: The time it would take to accumulate $13,000 by depositing $500 at the end of each month in an…

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Q: ind an equation of the tangent line to the graph of the function f at the specified point. 2 f(x) =…

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

Q: 7+n-2n² 7n² + 1 (Use symbolic notation and fractions where needed. Enter DNE if the sequence…

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Q: A particle moves along the x-axis and is defined as x(t) = f(y² - 8y-9) dy, where x(t) is measured…

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Q: Let f and g be the functions in the table below. g(x) 2 3 X 1 2 3 f(x) 3 1 2 1 (a) If F(x) =…

A: NOTE: Refresh your page if you can't see any equations. . the first function is  take derivative

Q: Evaluate 163i (3+6i)|

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Q: Find a unit vector that is parallel to the line tangent to the parabola y = x² at the point (6, 36).…

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Q: (a) J(X1, X2) X1X2 + 2X1 (b) g(x₁,x₂) = x1 + x2 sin 2x1 (c) h(x,y) = re* +2 tỷ (d) f(s, t) = (1+2s²…

A: We have to find the second derivative.

Q: 1 At a temperature of 20°C, the volume V (in liters) of 1.33 g of O₂ is related to its pressure p…

A: Given query is to find average rate of change and instantaneous rate of change at indicated point.

Q: Sketch a graph of ƒ(x) = −2|x +1| + 2. Before sketching the graph, determine where the function has…

A: We have to draw the graph for given Questions.

Q: Let f(x, y) = ln(x) + ln(y), r(t) = (cos(t), t³). Use the Chain Rule to calculate ƒ (r(t)) at the…

A: f(x,y)=lnx+lnyr(t)=<cost,t2>d dx(lnx)=1x

Q: Evaluate the integral. r9 S² dx 2 (x² - 1)3/2

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Q: Find the value of at which the tangent line to the curve y = +1 passes through the origin.

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Q: You invest $700 in an account in 2005. In 2013, the amount has increased to $819 due to interest.…

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Q: f (x) = 8 −x^4/1-cot(x) find the derivative

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) fee-t at dt

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Q: Let ƒ(x) = 3 cos(3x + 5). Find ƒ'(x).

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Q: Jo 4 cos* x dx

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Q: B. lim f(x) = x-0+ D. f(0) = F. lim f(x) = x→2+ H. f(2)=

A: Given query is to find indicated limits from the graph.

Q: The table shows values of a force function f(x), where x is measured in meters and f(x) in newtons.…

A: Work done(W)=∫abF.ds  where F is the forceds is the change in displacementa and b are the two limits…

Q: 3. (x + y - 6)dx + (x -y + 4)dy = 0.

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Q: Eliminate the parameter to find the cartesian equation of the curve: The equation of the curve is: y…

A: We need to eliminate the parameter to find the Cartesian equation of the curve.

Q: Calculate the first four terms of the sequence, starting with n = 1. Cn = (-1)²n+5 C1 = C2 = C3 = C4…

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Q: Let f'(x)= = f(x) = x² tan ¹(7x)

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Q: Use the Ratio Test to determine if the following series converges absolutely or diverges. (−1)n n²(n…

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Q: Use the Chain Rule to find dz/dt. dt || z = cos(x + 3y), x = 5t³, y = 4/t

A: Given :z=cosx+3yx=5t3 and y=4t

Q: 3. A force of 1500 lbs compresses a spring 6 inches from its from its natural length. Find the work…

A: Given that amount of force is 1500lbs to compress a spring 6 inches.

Q: Consider the following function. (If an answer does not exist, enter DNE.) f(x) = (a) Find the…

A: Given function :- fx=x2x-6

Q: 1. A survey of 50 athletes determined that 13 drank coffee, 18 drank tea and 6 drank coffee and tea.…

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Q: Calculate F'(0), where F'(0) F(x) = Hint: Do not calculate F'(x). Instead, write F(x) = f(x)/g(x)…

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Q: Find an equation of the plane. The plane through the point (3, 0, 4) and perpendicular to the line x…

A: The equation of line which is perpendicular to the plane is given as x=7t, y=3-t and z=5+6t. So, a=…

Q: 19. 10

A: Given query is to find the factors of the polynomial of the function.

Q: a varies directly as the square of b and inversely as the square of c. If a = 100 when b = 5 and c =…

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Q: Find the derivative of the function g'(x) =□ g(x) = = X 3x + -3 x

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