Use the cylindrical shell method to calculate the volume of the solid formed by rotating the graph of f (x) = about the y-axis on the interval 1, e]. 3 Note: Round to the nearest hundredth.

Q: Exact ODE y'=-4/x; y(2)=3

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Q: e^x(y'-y)=2xy^2 bernoulli differential equation

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Q: 4. (a) Show that the line l given by l: 1= 2+3t, y=1+4t, z= 5+ 2t, te R, lies in the plane II given…

A: Given problem:- Show that the line  given by   l : x = 2 + 3t , y = 1 + 4t , z=5+2t ,t in R   lies…

Q: Find the iimit oT X SP approaches zero from the left. x -3.62330136 t-0.827974189 4- 2 10 12 does…

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Q: B and C

A: Topic:- application of derivatives

Q: Find fx , fy and fz. 1 -1 f(x, y, z) = tan %3D \xy²z4, ().

A: Here we will find Fx,Fy,Fz;

Q: Find the dimensions of a rectangle with area 216 m whose perimeter is as small as possible. (If both…

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Q: 3) roțațion 90° counterclockwise about the origin

A: We know that,  90° counterclockwise rotation: (x,y) becomes        (-y,x)

Q: The base of a three-dimensional figure is bound by the line y = x +2 on the interval [0, 4].…

A: Let's find.

Q: Find a polar equation in the form r= f(θ) of the ellipse with eccentricity e= 6/7 such that one of…

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Q: 2, 22, 23 567 3. Test the series +. +.

A: Topic:- sequence and series

Q: The base of a three-dimensional figure is bound by the x-axis and the curve y = e on the interval…

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Q: Choose the correct speed and direction of a plane with a velocity of (-5,12) . 13,293° 17,113°…

A: Find your answer below

Q: Given f''(x) = 4x – 5 and f'(– 3) = 3 and f( – 3) = 6. Find f'(x) = and find f(3)

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Q: (e2y – y) cos a = e" sin 2r, y(0) = 0

A: Solution is given below:

Q: with A parti cle is moving a cc eleratoN at) = 12t+18. Its positian at time t = 0 IS S© =4 and its…

A: This question is related to integration, we will solve it using given information.

Q: f(x) = / sinx cos x

A: The objective is to flnd the derivative and slmpify.

Q: 1 dx so that the integral evaluates to - 3x2 integral / Ae2*- 2x³ – 3x² Replace the letter A in the…

A:

Q: 2. Determine whether the following integral is convergent or divergent. Do not guess! 4 dx x2 – x -…

A: To determine whether the following integral is convergent or divergent.∫04dxx2-x-2

Q: Consider the parametric equations below. x = t? - 5, y = 3 - 4t, -3 sts4 (a) Sketch the curve by…

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Q: 2. Find the radius of convergence and interval of convergence of the series. (a) (-1)--1 (" – 5)*+1…

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Q: Solve the differential equation. 4 + Vr du dr 5 + vu II

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Q: A plane traveling with a velocity measured in meters per second, is described by vector a = (-6,5) .…

A: Let's find.

Q: 2. f(x,y) = ye3x²+4y³

A: Given query is to find the fist order partial derivative.

Q: If A = [1 2 3], which type of the given matrix A ?

A: Given Matrix A=[1  2  3 ]1×3  Here number of row=1  Number of columns=3

Q: For 5, Sketch the region enclosed by the given curves. Find its area. Make sure you show how you…

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Q: a) Find the degree 4 Taylor polynomial T(x) for the function f (x) = 2e" centered at the point a 3.

A: Given that fx=2ex  centered at the point a=3we defined the nth taylor polynomial centered at x=a Tn…

Q: earning Task 1: Determine the derivative of the following. x*y + 2y3 = 3x + 2y %3D

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Q: 2. The function g(x) is defined for -3Sx5 3. The behaviour of g'(x) and g"(x) is given below.…

A: A)-3<x<-2, g'(x)<0and-2<x<1, g'(x)>0Function decreases over (-3, -2) andincreases…

Q: dy = (Type an integer or a simplified fraction.)

A: Topic:- double integration

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 5y2 + 10, (3, 4) Vf(3, 4) еBook

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Q: -8 17 sine -15/17 -8/17 15/17 8/17

A: Given query is to find the measure of indicated angle.

Q: e*(y' – y) = 2xy?

A: Given

Q: find the derivative of y = x3/x

A: Given y=x3x

Q: The sum of two numbers is 8. The product of the first number and the square of the second number is…

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Q: Find the limit of s(n) asn→ 0, 4 s(n) = n3 n(n + 1)(2n + 1) 8

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Q: At which points on the curve y = 1 +°40x³ – 3x³ does the tangent line have the largest slope? | (x,…

A: Maximize slope

Q: How 2 Find the absalute maxima and minima for the funcfion f(x,y) 48xy-32 x - 2u yen the…

A: Find value at critical point and end points.

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. sin…

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Q: 3dt 1. J (2r+8) fr+1 Suv-2+1 ¢v 25x -9 dx 3. 4. V40-4v-v dv

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Q: Find the radius of convergence, R, of the series. n- 1 R = Find the interval, 1, of convergence of…

A: We have to find the radius of convergence R for the given series…

Q: 2. The function g(x) is defined for -3 Sxs 3. The behaviour of g'(x) and g"(x) is given below. -3…

A: To answer the given question using the given tables of g'(x) and g''(x).

Q: Find the general solution: dy = tanxtanydx %3D

A:

Q: Streaming Music Consumers are spending more on music from digital sources than they do on CDs.…

A: f(t) =3.7+ln(t+1)(a)in 2012 , t=0f(0)= 3.7 +0.84 ln(0+1) = 3.7+ln1=3.7+0f(0)=3.7Amount spent by…

Q: 4 1 4. |x2ydxdy 2 0

A:

Q: what is the area between the curves: y = 7 cos( pi*x),    y = 12x2 − 3

A: 7cos(πx) and 12x2-3

Q: Let f(5) = 6 and f' (x) <8 for all z between 5 and 16. Use the Mean Value Theorem to find the…

A: Mean Value theorem: If f(x) is a function that satisfies the followings.      (i) f(x)  is…

Q: 40- 4v-v dv

A: ∫xn dx =xn+1n+1+C ∫cos(ax) dx =1a sin(ax)+C

Q: 3. Find the orthogonal trajectory for the family of straight lines passing through (3,-5).

A: