Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations y = x2 and y = 6x- x2 about the given lines x-axis and y=6. A. 37π B. 27π C. 17π D. 47π

Q: Show that the following series is divergent using the Test for Divergence. 4k³ - 1 k³ + 5k² + k k=1

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Q: State the order of the given ordinary differential equation. d²y dx² dy = 1+ dx. Determine whether…

A: We know that :-  The ORDER of a differential equation is the order of the highest  derivatives that…

Q: 2. gxc2x2+3 dx Selast & du 니 get x in terms of u ut 2x2 +3 4-3 = ㄹ x² 4-3 x = 이들 4-3 z soke har x…

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Q: Find the derivative of each of the following functions using any method. 7.) f(x) = 6cot(sin(4x))…

A: 7. fx=6cotsin4x8. fx=6sec7x29. fx=e6x2-17

Q: Find dy/dx by implicit differentiation. /xy = x³y + 73 dy/dx =

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Q: 3t 2t - 1 1-t 1+t [][] 3 and B(t) = 51² 51³ t Verify the product law for differentiation, (AB)' =…

A: See the details solution in below

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Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

A: According to company's rules, I need to solve first question when multiple questions are posted.. So…

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Q: Solve the given differential equation by separation of variables. dy xy + 3x - y - 3 dx xy - 2x + 4y…

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Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i-2j+ 2k. 1, Find the unit vector…

A: We can solve this as follows:

Q: 1. Determine whether the series n=1 3n+1 ln(n+1) is convergent or divergent.

A: : since,1< ln(n+1),for n>2 so, 0<(n^2)/(((3^(n+1))*ln(n+1))<n^2/n^4=1/n^2,  since…

Q: -0.5 1 100³S 1-=X² dx represents the area of a region bounded by 1 O a. the vertical lines x = +0.5,…

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Q: 니 - ****** سر ** x² coscyldy dzdx

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Q: Find the solution of the given initial value problem. ㅠ ty' + 2y = sint, y (-) - = 5, t > 0 Y ||

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Q: Find the solution of the given initial value problem in explicit form. 1 y′ = (1 — 13x)y², y(0) = 6…

A: We can solve the given initial differential equation .

Q: Find the value(s) of k that makes the given function continuous. 4x 5 if x < k f(x) = { = x++1 ifk…

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Q: 41 - S™ SX SX² *S* x² cos cyldy d z d x

A: Let's evaluate given triple integral.

Q: 15. Yogurt containers can be shaped like frustums. Rotate the line y = x around the y- axis to find…

A: 15.   yougurt containers can be shaped like frustrums.Rotate the line y=1mx around the y-axis…

Q: Find the arc length of the curve y = 2/3 (x − 1) raise to 3/2 on the interval [2,3]

A: We have to find the arc length of the given interval [2,3] .

Q: You are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by…

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Q: 1 (c) I Y (d) y = 5x x², y = x = 0, y = 1, y = e I=

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Q: 8) S dx it sinx + cos x a) in (1 + tan =) + c b) In (i - tan £) + c c) - In (1 + tan x) + o 2 d.)…

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Q: The following limit gives the derivative of a function f(x) at a point xo: lim h→0 (2+h)³-8 h -8)…

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: 3. Compute the net area of the following function on the given interval. f(x)=x²-4; [-2,2] -14 <-2…

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Q: 2.) Determine whether the geometric series is convergent or divergent. If it is convergent, find its…

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Q: Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the…

A: The objective is to solve the above question.

Q: 1. J tanßsec2ßdß 2. (tan0 – 1)2d0

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Q: In the year 2000, the population of a small city was 40,000. The population grows at a rate of r(t)…

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Q: Find y'. tan(x + y) = x + y

A: Solution ) tan ( x + y ) = (x + y ) Differentiate with respect to x d/dx tan ( x + y ) = d/dx ( x +…

Q: Find the general solution of the given differential equation. xdy-y=x² sin x yw Give the largest…

A: Explanation of the answer is as follows

Q: Q6) Use Gauss- Jordan Elimination method to solve the following linear equations. 2X + 2Y = 2…

A: Solving the problem by finding the value of the problem.

Q: Find the Taylor series expansion of f(x) = ln(3-2x) about a = 1.

A: The function f(x) is given by, f(x)=ln(3-2x) Differentiating the function successively upto n…

Q: d²y Find for the following function. 2 dx y= (3x² +1) -5 d²y dx² =

A: On solving this we will get

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

A: The objective is to solve the above question.

Q: Solve the given differential equation. All solutions should be found. dy 3x² – 2y - y³ 2x + 3xy² dx…

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Q: If the tangent line to y = f(x) at (5, 2) passes through the point (0, 1), find f(5) and f'(5). f(5)…

A: Topic = Derivative f5=2f'5=15

Q: Q5) Solvex+2xy = 3 by using Euler's method to find he approximate solution up to X-2.9 when h = 0.5…

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Q: 5(c) Find the rectangle with the largest area that can be inscribed in the top half of the ellipse ²…

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Q: You are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by…

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Q: c) S xaccainxdx a) = (2x²-1) arcain x + ¥√√√²-x² + C b) 42 (2x² +₁) ancais x + x²√√1-x² + c c) 4…

A: The objective is to find the integration.

Q: 17. A spring has a natural length of 20 cm. A 40 N force is required to stretch (and hold the…

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Q: [ (cosx+2sinx) COSX dx

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Q: A company discovers that to produce a = 890 new electronic parts, it will cost y = 980 new…

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Q: The graph above is a transformation of the function f(x) = Write an equation for the function…

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Q: Given the equation z = arctan(x- y²) with the change of variables x=s³-t³ and y=st² + s²t, use the…

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Q: Solve the given differential equation. All solutions should be found. dy 3x² - 4y - y³ 4x + 3xy² dx…

A: Explanation of the answer is as follows.

Q: For the next three series, (a) determine the radius of convergence, (b) determine for which the…

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Q: Fill in the blank. The symbol C₁ represents a constant. - (6 + C₁e-⁹x)= Write this result as a…

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