VOLUME Example: ◆ The region bounded by the parabola y = x¹/2 y = 1, and x=4, is revolved about y = 1. Find the volume of the solid formed. " R(x)=√x-1 y=Vi Ja E II-1 Rix) - Vx-1 GR (x, 1)

Q: Let F(x) = f(x¹) and G(x) = (f(x))¹. You also know that a = Then F'(a) = = 12, f(a) = 3, f'(a) = 4,…

A: Fx=fx4 and Gx=fx4a3=12, f(a)=3, f'(a)=4, f'a4=7

Q: Suppose a population of fruit flies changes at a rate of g(t) = -4e0.041, in flies per day. If the…

A: Here we have a population of fruit flies that changes at a rate of g(t)=-4e0.04t…

Q: Given the differential equation y²dx + (3xy + y² − 1) dy = 0 What is value of SM ? dy

A: Given the differential equation, y2 dx+3xy+y2-1 dy=0To find the value of δMδy.

Q: Problem 7 x√x + 1 dx

A: Given ∫07xx+13dx

Q: Suppose P(t) represents the population of a certain mosquito colony, where t is measured in days.…

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Q: dy dx + y = 2xy-ex

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Q: ог Question A.) Does this CONVERGE • DIVERGE ? (~) ² M nal

A: To determine whether the given series converges or diverges.∑n=1∞ln n2n

Q: Using integrals, find the area bounded by the following:  f(x) = 4x2 + 20 g(x) = 8x + 32 x = - 4…

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Q: (b) Find the area of the region that lies inside the first curve and outside the second curve. r = 1…

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Q: The angle between vectors A = 91-j+5k and B = (-2,7,1) is.. ******

A: According to our terms and conditions,we can only solve one problem at a time. So please repost the…

Q: Find the area of the surface obtained by rotating the line y = 19x + 6 about the x - axis from the…

A: Area of surface is evaluated.

Q: Use the elimination method to find all solutions of the system: [x² + y² = 7 x² - y² = 4 The four…

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Q: 2. Find the area of the region between the curve, x = y² + y −6, y- axis and y=0; y = 3.

A: we need to find the area bounded by the given curves.

Q: 9. f √x³-1dx x

A: Given: I=∫x3-1xdx    ...1 As we know that; ∫11+x2dx=tan-1x+C

Q: y = tan (xxy) -1

A: We have to evaluate the following differential equation.

Q: 11.J sin 3 x sin 6 xdx 3

A: To evaluate the given integral.∫sin 3x sin 6x dx

Q: 0 Q2. Find the exponential Fourier series for f(t) = { 1<t<2 Fourier series. then find the…

A: Fourier series is given.

Q: Q2: A. Determine if p = ï-3k and q = 61 - 3j-4k are parallel, orthogonal or neither. B. Find the…

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Q: Question 36 To integrate x³ ex dx, we apply integration by parts and in the form u dv, dv is set as:…

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Q: y = (4 + ³√/x)³ 3

A: Inverse function

Q: 2. +4y= sin(3t), y(0)=2, y'(0) = 0

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Q: Use the graph of f and g. p(x) = f(x)g(x) f(x) g(x) = - g(x) 101 8- 2 0 -2 2 (a) Find p'(9). p'(9) =…

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Q: Solve what is asked in the following problems. Write your solutions and box your final answers 1.…

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Q: Find the slope of the tangent line to x+y=10 at (1,8).

A: According to our guidelines , we can answer only first question. Kindly re-post other remaining…

Q: Reverse the order of the integration ² dy dx + 2 dy dx equal:

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Q: Find a + b + c. The Maclaurin Series for f(x) = ln |3 + 4x is: f(x) = lnb + 26 + Σ'()"

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Q: SOLVE THE FOLLOWING HOMOGENOUS LINEAR DIFFERENTIAL EQUATION:

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Q: Specify the domain of the function f(x)=sqrt2x+10   The domain of f(x)fx is x

A: Here we need to find out the domain of the given function.

Q: Find the line integrals of F = 4yi + xj + zk from (0,0,0) to (1,1,1) over each of the following…

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Q: s={ 3112 4'2'3'9' =(5, 5.5, 6, 6.5, 7, 7.5,...} = {√2,2√2,3√2, 4√2,...} ={√2,2,2√2,4,...}

A: Topic:- sequence and series

Q: 6. Find of z = In(xy) 8²y

A: Given:       z=lnxy     ∂z∂y=∂∂ylnxy  Treat x as constant  Apply chain rule:…

Q: 9.f tan3³ x √sec x dx

A:

Q: bject is dropped from a 150-foot-high building, its position (in feet above the ground) is given by…

A: Please refer to the image below

Q: Make Detailed solution TECHNIQUES OF INTEGRATION

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Q: Find the dimensions of the largest rectangle that can be inscribed in an isosceles triangle if one…

A: We need to find dimension of rectangle.

Q: Question. Suppose a population of fruit flies changes at a rate of g(t) = -3e0.021, in flies per…

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Q: = Use the Riemann's Criterion for integrability to show that the function f(x) integrable on [0, b]…

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Q: answer the related questions. 7. ул y = G(x) 3 10 + N grap -2 -1 0 4 5 a) Find lim G(x). x-3+ b)…

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Q: 3.§ sin* 2 x sin 4 xdx

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Q: dy : Find the for the following functions: dx 1- y = e(x+ln 5x) 2- y = cosh-¹ sin 2x 3- y = xsinh x

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Q: Q1: A. Find the general solution of the following Initial Value Problem (IVP): y+9y-10y = -40t²-72t…

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Q: A bicycle with 24-inch diameter wheels is traveling at 16 mi/h.   Find the angular speed of the…

A: Given Problem:- A bicycle with 24-inch diameter wheels is traveling at 16 mi/h. Find the angular…

Q: Determine the values of m and b such that function g is continuous at every real number: if r 1.

A: Since the function g is continuous.So, limx→1-g(x)=g(1)limx→1-x2-mx=-212-m(1)=-2m=1+2m=3

Q: Find the gradient field of the function g(x,y,z) = 8xy + 2yz + xz. Vg= (Type your answer in terms of…

A: We have to find the gradient field.

Q: d²y dy 4. (a) Compute the general solution for: +4 dt +3y=e-t/2. dt² (b) Compute the solution with…

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Q: 6-18x4 ic notation and fractions where needed. Give your answers in the form of comma separated li…

A: Topic:- calculus

Q: Use Figure 1 to evaluate each trigonometric function of angle AA. The side adjacent to angle AA has…

A: Given; The side adjacent to angle A has length 4 and the side opposite angle A has length 14.

Q: The partial fraction decomposition of f(x) g(x) + where 3 (x + 3) (x² - 4x + 4) f(x) = g(x) = -3x² -…

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Q: tan² y = x (By implicit differentiation)

A: The given equation is tan2y=x.

Q: d the area of the surface obtained by rotating the line y = 19x + 6 about the x-axis from point…

A: Topic:- application of integration