A region bounded by the following curves is revolved around the y-axis. Use cylindrical shells to find the volume of the solid generated. y = V36-x², y = 6 and x = 6

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Q: Solve the given differential equation by separation of variables. dy ху + бу — х — 6 - - dx ху — 5у ...

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Q: Use partial fractions to find the indefinite integral. 9 – x2 dx 5x3 5x + X

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Q: Use the ratio test to determine whether the series converges or diverges. If the test is inconclusiv...

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Q: Q5) A) Graph the curve Y = - 2 x (x - 4)(x + 6)(x - 2) between the value of x [0, 4], then find the ...

A: Solution

Q: ) Graph the curve Y = x (x +5)(x -3) between the value of x [-5, 3], then find the area of the finit...

A: Area under the curve =∫ab(upper curve -lower curve)dx  

Q: Find the domain of a function of the form f (x) = va – x².

A: Given function:- f(x) =√(a-x2)  To find:- Domain of given function f(x) 

Q: Write the first five terms of the sequence: +Do |{vn² + 10n – n}, n=1 Determine whether the sequence...

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Q: Find the indefinite integral. (Use C for the constant of integration.) sin4 20 de

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Q: A. Find the following limits: 2t2+3t+1 iii. lim 2t-1

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Q: Verify that the indicated function is an explicit solution of the given differential equation. Assum...

A: Given:     y''-6y'+25y=0     y=e3xcos4x      y'=ddxe3xcos4x  Apply the product rule: ux·vx'=u'x·vx+u...

Q: (iii) What quantity q maximizes revenue? What is the maximum revenue?

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

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Q: ) Evaluate the following integral: S V2 + sin 3t cos 3t dt

A: We have to find solution of given integral.

Q: Using appropriate substitution, the integral S e t3 dx is equal to:

A: ∫ex-3dx/x4 now substitute u = x-3 du/dx = -3/x4 dx = -x4du/3 ∫ -eudu/3 (-eu)/3 + c now put value of ...

Q: Find the radius of convergence of the power series. (If you need to use co or -00, enter INFINITY or...

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Q: n Express lim e"/n² re/n? as a definite integral. i=

A: The solution is given in the next step.

Q: Question * Using integration by parts, the integral Sxsec(2x) tan(2x) dx is equal to:

A: The integration of the integral is xsec(2x)tan(2x).

Q: Compute the angle between the two planes 2x + 3y + 7z = 2 and 4x - 2y + 2z = 4.

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Q: Fill in the table with the correct information by referring to the function f below. The table conta...

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Q: Q3) A) Graph the two equations and find the points in which graphs intersect x+y = 0, y= -(x- 1) TA ...

A: A) The graph is shown below:

Q: 2. Form the differential equation from the circle passing through the origin having their centers on...

A: This question is based on forming differential equation by eliminating constant.

Q: f(x) = X-5 if xŹ 2 at x = 2 2x if x< 2

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Q: + - Consider (x. Using u-substitution and transformation of integrand, then the power formula applie...

A: Here we have to find values of  K,n from the integral after U substitution as shown below

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A: Here x = independent variable y = dependent variable k = y - intercept = ( 4.5 0.1) m/s2

Q: Use the limit comparison test to determine whether the series converges Σ 7k + 5 k=1 The series

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Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = xo and then find the nth Taylo...

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Q: Consider the relationship 7r+4t=21.   a. Write the relationship as a function r=f(t).   Enter th...

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Q: C_B* O UI

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Q: Given: -dx. Using u-substitution and transformation of integrand, what is u and du? 3/x - 2x 3 (A) u...

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Q: Question 16 Find the area of the parallelogram with the two adjacent vectors, a and b, to the neares...

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Q: Problem 2: A piece of string whose length is given below is cut into two pieces. One piece is used t...

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Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

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Q: II. For each of the following functions, find the indicated derivative using the definition. Show so...

A: As per our guidelines we are supposed to answer only ? 3 sub- parts ( if there are multiple sub- par...

Q: sinx dx TI Cosx t ecoS X 2. e cosX

A: integration

Q: Sec2X Q1) A) Evaluate the following integral: S V1-tan2x B) Find the slope of the line tangent to th...

A: A) the given integral is sec2x/√(1-tan2x). B)y=Sin5x ; x=π/3.

Q: 10. y'+y = 3x³ + x; y(-1) = 4 су 3 3х3 + х; у(-1) %3D4

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Q: Score Grade/Section: Date 13. What is the solution of the inequality? A. x > -1 or x 1 or x -2

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Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about %3D x = xo and then find the nth T...

A: Taylor polynomial

Q: n (a) Express lim as a definite integral. i=1

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Q: By completing the square, dx tegral J_2 x2+4x+5 is equal to=

A: ∫-2-11x2+4x+5dx

Q: х3(1 — х)8dx

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Q: Problem 2: A piece of string whose length is given below is cut into two pieces. One piece is used t...

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Q: . Find two positive integers such that the sum of the first number and four times the second number ...

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Q: Determine whether the series converges; if so, find its sum. If the series diverges, indicate that w...

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Q: Tutorial Exercise Find the indefinite integral using integration by parts with the given choices of ...

A: As we know that; The Power law; ddxxn=nxn-1 And ∫sinax+bdx=-1acosax+b+C∫cosax+bdx=1asinax+b+C Where,...

Q: 3. Find and and y= ivative of

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