Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. y = 0, x= 1, x=3

Q: K石Xuts

A: ∫ Sin-1 x dx   ....(1) Using integration by parts ∫ f1(x)*f2(x) dx = f1(x)∫f2(x)dx-∫[d/dx(f1(x)*∫f2(...

Q: Find the value of k so that the value of f,"(2y – 1) dy is 10. 1 2 4 A) в B) c A D) D 3.

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Q: Question 16 dx What should be the rewrite of the integrand of S so that the resulting integral is in...

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Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: An object is shot upwards from ground level with an initial velocity of 3 meters per second; it is s...

A: Let's find. 

Q: (2xy-tany)dx + (x² – xsec*y)dy = 0; y(1) = *

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Q: CALCULUS A. How do you define Differentiation? B. Explain the principle of derivative with a given f...

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Q: 13

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Q: Question 5 The slope of curve is given as (2x + b + 5) and has a value of at x = 2. What is the valu...

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Q: The slope of curve is given as (2x + b+) and has a value of 17 at x = 2. What is the value 16 of y w...

A: Topic = Integration

Q: Evaluate f*27 dx. x+3 A.) + 9x + C B.) 3 3x2 + 9x + C 3x2 C.) 9x + C 2 3x2 D.) ++9x + C I + +

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Q: Find the antiderivative of 5sinx In 5 cos x dx. A.) 5cosx + C B.) 5sinx + C C.) 5sinx In 5 + C 5sin ...

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Q: x* + x³ + x² – x + 1 x(x² + 1)²

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Q: 2. (D2 + 3D)y = -18x; y = 0, Dy 5 when x

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Q: Hannah buys 2 dozen roses. Of these roses, are red, and the rest are white. How many white roses doe...

A: We need to find number of white roses.

Q: Evaluate f x+3 x3+27 dx.

A: Our Aim is to evaluate the integral given below:-∫x3+27x+3dx -(i)

Q: Calculate the first-order differential equation below using transformation y = xv. dy x+3y = 2x – y ...

A: We need to solve the D.E.

Q: An open-box with a square base is to have a volume of 500 cubic inches. The material for the top and...

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Q: 1. Find the indicated values. f(g(8)) |x| f(x) g(x) s(8(5)) 1 5 g(f(5)) 2 5 8(5(3)) 3 2 4 4 1 S(S(4)...

A: Use the given table for finding the value of function 

Q: Find all local extrema for the function f(x,y) = - 6x - 9xy - 4y + 72x+54y+ 6.

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Q: * Limits of Polynomial, Rational, & Radical Functions Evaluate the given limits. 1. lim Vx+ 16 X-7

A: Here we have to evaluate the given limit.

Q: P(z) how might the function 9(x) Question 3: When working with rational functions of the form f (x) ...

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Q: Solve each equation for x. (For each answer, enter an exact number. (a) e5x + 9 - 4 = 0 X = (b) In(4...

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Q: Test the series below for convergence using the ratio test. 5n n! n=1 The limit of the ratio test si...

A: Given:     Equation is given

Q: 18( cos54 + isin54°) 3(cos102" + isin102" )

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Q: Let s = f(t) give an object's height, in feet, a seconds after it is thrown. After 3 seconds, tE fee...

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Q: 15. A particle moves along a straight line and has acceleration given by s"(t) = 5t + 3. Its initial...

A: A particle has acceleration s''(t)=5t+3Initial velocity is s'(0)=-4 cmsecinitial displacement is s(0...

Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by L(x.y) =x +y -...

A: Given: Suppose the labor cost in dollars for manufacturing a camera can be approximated by Lx, y=32x...

Q: dx What should be the rewrite of the integrand of so that the resulting integral is integrable? ... ...

A: ∫dx1+cosx

Q: A series RLC circuit is shown in Figure Q4 (b) where R= 4Q, L = 0.5H, C= 0.1F,E(t)=10 V and i(0) = 0...

A: Given: R=4ΩL=0.5 HC=0.1  FE(t)=10 V

Q: Vx+3 4. f(x) = f'(1) x-4

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

Q: 5х —7 (х — 3)°

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Q: 19. Find the total area between the parabola y = x2 - 4x, the x-axis, and the ordinates x = -2 and x...

A: We can use integration to calculate the area

Q: Order these functions by time their complexity in ascending order 3n .2 n5:nº lg°(n), 54log25 (n) n2...

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Q: Compute the partial sums S2, S4, and S6 of 1 1 + 3.4 1 1 + + 5.6 2.3 4.5 (Use symbolic notation and ...

A: Given:-     To find:- S2  S4  S6

Q: d²x dx 5 dt2 2- 3x = -9t2 – 1 - - dt dx When t = 0, x = 1, = 0, find x when t = 2 dy %3D -

A: Please see the below picture for detailed solution. 

Q: What is the value of a so that In (e") dx 6? ... A.) 0 В.) 1 C.) 2 D.) 3

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Q: Vx+3 4. f(x) = **3 f'(1) x-4

A: Given:- f(x) = √(x+3)/(x-4)  To find:- f'(1) 

Q: Forms of Summation Notation 5. Sum of the squares of the variables: Ex = x,² +x,' +..+x,² i=1 Exampl...

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Q: Using incremental search with x1 = 1.5 and Ax = 0.01, %3D %3D approximate the solution of Inx = = 2-...

A: fx=lnx - 2+xx1=1.5∆x=0.01tolerance=0.05----------------Find: To find 'x=a' such that fa = 0±0.05.  -...

Q: x²-16 Find k so that f(x)={ x-4 is continuous for all x. k = k ;x=4

A: Given,f(x)=x2-16x-4;      x≠4k          ;       x=4 Here f(4)=4limx→4f(x)=limx→4x2-16x-4limx→4f(x)=l...

Q: Find the antiderivative of 5$sinx ln 5 cos x dx. A.) 5cosx + C B.) 5sinx + C C.) 5sinx In 5 + C 5sin...

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Q: (a) Calculate the first-order differential equation below using transformation y = xv. dy +3у %3D 2х...

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Q: 16. 5dx If +1= 2-, what is the value of b? 4 V8x2 a.) 2 b.) 4 c.) 8 d.) 9

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Q: Let X be the set {5, –6, 2}. For the first three parts of this problem you are asked to define a fun...

A: Consider the set 5,-6,2. The function is f:X→X and the relation is u~w⇔w=fu.   a) The relation is re...

Q: Suppose f is a quadratic function that has roots x = – 3 and x = 6, and f(0) = 15. We will w a funct...

A: Given: Root x=-3  and x=6 f(0)=15

Q: Compute fx, fy: f (x, y) = arctan(xy)

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Q: Find

A: Solution is here

Q: the rate of change in thr profit (p) with respect to the number of units sold (x) is 0.0006x^2 +10. ...

A: We can use the given equation to solve for profit

Q: Determine if the given function is continuous on each of the given intervals. A. f(x) = 3x³ + 4x² - ...

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