Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the curves about the given axis. y = Sex, y = Sex, x= 1; about the y-axis

Q: Differentiate. y = In (4x² - 7x+9) y'=0

A: The function is The aim is to find the derivative of the function

Q: The total cost (in dollars) to produce q units of a good is given by the function: C(q) = 4.9q +…

A: Given, C(q)=4.9q+41000

Q: The view V, or distance in miles, that one can see to the horizon from a height h, in feet, is given…

A: The view V, or distance in miles, that one can see to the horizon from a height h, in feet, is given…

Q: The sum of the geometric series 7 + 21 + 63 + ... + 413 343 is 826679 620011 413 434 1860 040

A: Formula for geometric series is given as follows nth term of GP is given as follows Sum of n terms…

Q: Find the vertex, focus, and directrix of the parabola. ​(x+3)+(y-1)^2=0

A: The given equation of parabola

Q: Find the derivative of g(a) 32x-1 5 1 6x²-3x+1/

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Q: 1. Let a=⟨0,1,−5⟩ and b=⟨4,0,1⟩. Compute: 3a+4b=⟨ _____,_____ ,______ ⟩ |a|= __________

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Q: Use spherical coordinates to find the volume of the smaller wedge cut from a sphere of radius 9 by…

A: To findThe volume of the smaller wedge cut from a sphere of radius 9 by two planes that intersect…

Q: Assuming that the equation below defines y as a differentiable function of x, find the value of…

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Q: (a) (c)= dx (c) & √(x²). (e) d [ƒ(g(x))]= (g) (sin x)= dx (i) --(tan x) = dx d (k) (sec x) = dx (m)…

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Q: 7. Find an equation of the plane that passes through the following three points P₁ = (2,5,1), P2=(3,…

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Q: dz дz Find the values of and at the given point. дх ду 2z³-4xy + 5yz + 2y³ - 35= 0, (3,3,1)

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Q: 1. Solve the equation between 0 and 2, 3 sin²(x) + sin(x) = 1 − 3 sin²(x)

A: We are given the trigonometric equation and need to solve it.

Q: Consider the function f(x) = 23. Which of the following functions are equal to f(x)? Select all that…

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Q: Find equations for the line perpendicular to the plane x + 5y - 2z = 6 and through the point of…

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Q: 1. FIND THE AREA DEFINED BELLOW (a) y ≤ 5 2(x²+1) y=1-1/2/2/2 L y²1-x x 20 (b) BOUNDED AREA BETWEEN…

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Q: Can you do part d) and e)

A: The linear equation is given by:

Q: Set up (but do not evaluate) an integral that expresses the area between the circles 2 2 2 2 x + y²…

A: To find the area between the circles x^2+y^2=2 and x^2+(y−1)^2=1, you can set up a double integral.…

Q: The unit cost, in dollars, to produce bins of cat food is $12 and the fixed cost is $23546. The…

A: Given that the unit cost, in dollars to produce bins of cat food is  and fixed cost..The price…

Q: a kite 50ft above the ground moves horizontally at 9ft/s; at what rate is the angle between the…

A: A kite 50ft above the ground moves horizontally at 9ft/s. To determine the rate at which the angle…

Q: Find the general solution of the differential equation, y" + 2y' + y = e 2x for x > 0.

A: The general solution to a(x)y'' +b(x)y' +c(x)y=g(x) can be written as

Q: Find the volume of the solid obtained by rotating the region bounded by y = 7x², x = 1, x = 4, and y…

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Q: Find the derivative of the following function using the Fundamental Theorem of Calculus. F'(x) =…

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Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. S…

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Q: Write the given expression as the cosine of an angle. cos 45 degrees cos 40 degrees + sin 45 degrees…

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Q: 30. Prove or disprove: The derivative of y = sinx+cosx COSX dy is dx || 1 (1+sinx)(1−sinx)

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Q: sunscreen sales 12 eTextbook and Media Explain why the graph is periodic. We expect sunscreen sales…

A: The distance on the number line on which the function repeats itself is called the period of the…

Q: can you find C if x = 1/2 and y = (square root of 2)/2 thank you so so muchh!!

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Q: ow For the functions w = xy + yz + xz, x=u+v, y=u- v, and z = uv, express and using the chain rule…

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Q: Find two positive real numbers whose product is a maximum. (Enter your answers as a comma-separated…

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Q: A function f is said to have a removable discontinuity at a if: 1. f is either not defined or not…

A: The given function is; f(x)=(2x2+3x-14) /(x-2)

Q: Find the unit vector a) that makes an angle of (-3pi/4) with the positive x-axis b) obtained by…

A: To find the unit vector that makes an angle of (-3π/4) with the positive x-axis:Using the formula…

Q: Write the quadratic function in standard form. f(x) = 2x² - x + 1 f(x) = Sketch its graph. -10…

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Q: Find the derivative of the function at Po in the direction of u. x-y xy +3' g(x,y) = Po(2,-2), u =…

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Q: For the curve given by r(t) = (2 sin(t), -3t, -2 cos(t)), Find the unit tangent T(t) = ( Find the…

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Q: The following differential equation is a Euler equation. Find the general solution of x²y" — xy' + y…

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Q: Express the integrand as a sum of partial fractions and evaluate the integral. S 23dx (x²-1) ²…

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Q: Let g(u) = 8u +4 Determine the derivative of g.

A: The given function is,

Q: Use Simpson's Rule and all the data in the following table to estimate the value of the integral X y…

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Q: Express the sum xx²x³ + x² + x5-x-x² + x³ + ... 4n 4n-1 in terms of geometric series (hint: group…

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Q: Find the volume of the solid bounded by the graphs of x² + y² = 4, z = 4x + 5y, and the coordinate…

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Q: Consider the following function: f(x) = (x + 5)² (a) Express the derivative of f(x) at a point x =5…

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Q: др Draw a dependency diagram, and write a chain rule formula for and əm up am = с. др др ди = am du…

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Q: b) x+2 4 x-2 6 = 2x-1 3

A: Given,

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 5t²i – 3tj + _t3k (a) r(t) 5ti - 3j +…

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Q: Differentiate. y = dy dx In x11 12 4

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Q: Let the demand function for a product be given by the function D(q) == 1.6q+ 220, where q the…

A: Given demand function, D(q)=-1.6 q+ 220.Given fixed cost of production for the item is $3000 and…

Q: The function y(t) = 4e³t - 2e5t is a solution (but not the general solution) to y" + py' + qy = 0.…

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Q: · 2 * 2 of -2 2 $ The graph above shows the base of an object. Compute the exact value of the volume…

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Q: f(z) 2+3x1x², find f'(5).

A: f(x)=2+3x−4x2, find f′(5).