Q4 Calculate the volume of the solid obtained by rotating the region bounded by the parabola y = x(2-x) and the straight line y = 0 around the x-axis

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Q: Let f be continuous and twice differentiable function such that f is increasing and concave down and…

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Q: Find the general solution to 3y''+xy'+y=0 in the form of a power series around the ordinary point…

A: Note: this x0=0 is an ordinary solution. Let us assume that:y=∑n=0∞Cn(x-0)n…

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Q: 25 (6x + 5)³ But Do NOT use the Quotient Rule. a) Let f(x) = = f'(x) = Find f'(x). b) Let g(x) = 6…

A: We have to find the firstd erivative of the given functions.Recall some basic formulas: ddxxn=nxn-1…

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A: We can find the partial derivative of the function .

Q: Find all second-order partial derivatives for the function r = In |5x+y|. XX xy 11 = 25 (5x + y)²

A: Given function:- r=ln5x+y

Q: 7x – 4x − X

A: Topic = Integration

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A: It is known that derivative of a function represents the rate of change of the function.

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Q: Evaluate the limit: lim 02 does not exist lim √(0+1)²-1. Q→-2 0 1 0

A: Put Q= -2

Q: Answer

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Q: 01 O-3 O 733 113 It is known that function f is an increasing function that satisfies f(1) = −3 and…

A: Given:      f1=-3      f-11=3 we know that       f-1'y=1f'x

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Q: Use the Ratio Test to determine whether the series converges absolutely or diverges. 3(k!)² 5(2k)! 8…

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Q: Exercise 1 (1+4) ³-1 h The given limit lim h→0 Definition of the derivative represents the…

A: Given; Limh-0[(1+h)2/3-1]/h.

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Q: Write Z₁ and Z2 in polar form. 11π - 4( cos( 11 ) + sin ( 1 )) i 11π 6 Z1 = Z2 Z1Z2 = Z1 Z2 Z₁ =…

A: you should write a bracket

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A: Let $P amount be invested at r% interest rate compounded semi annually then after t years it will be…

Q: Answer the following Questions: 1. Evaluate the integral using partial fractions method: ²+1)…

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Q: 3.) Find y(4) if y=3x³ +2x² −x+9

A: Topic = Derivative

Q: determine the values of r for which  erx  satisfies the differential equation, we substitute  f(x)…

A: To determine the values of r for which the given function is a solution of the differential…

Q: Let z = f(x,y) = 15x² - 25xy +9y². Find the following using the formal definition of the parti əz ду…

A: All the subparts are solved below

Q: Find the maximum and minimum values of the function g(0) = 60 – 9 sin(0) on the interval [0, π]

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Q: | r - 1 dr

A: To evaluate the given integral.

Q: Approximate the area between the x-axis and the graph of f(x) = x² + 3 over the interval [0, 2] by…

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Q: Based on the data shown below, calculate the regression line (each value to two decimal places) y =…

A: Here for the given values.The best fit values for the regression line are- Slope =1.106 ± 0.08099…

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A: According to given graph  At x = 1 Given graph goes to 0

Q: A baseball team plays in a stadium that holds 50000 spectators. With the ticket price at $8 the…

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Q: Also

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Q: {2, y) = tans (2 I

A: Please see the below picture for detailed solution.

Q: 100 Determine, with full justification, if $19 da converges.

A: We have to find the following conditions according to the given information

Q: 7x sin²(x) dx =___________ (Apply integration by parts method) O 7x tan(r) 7x cot (x) 7x In(sin(x))…

A: Topic = Integration

Q: (5+51)³

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Q: Find the solution of the following differential equation. 1. (x² - 1) + 2y (x + 1)²

A: As per our guideline we can solve one question you can repost other question

Q: 5. Find the inverse function of f(x) = 3x - 7. 3.2.1) mont noita ovitostjd a (ewors diw) Jou Maitsa…

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Q: DDD

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Q: The vertical displacement of a particle attached to a spring is governed by the following second…

A: NOTE: Refresh your page if you can't see any equations. . here we have   for the homogeneous…

Q: In Exercises 13-18, use an inverse matrix to solve the system o linear equations. 13. x + y + 2z = 3…

A: The objective of the question is determine the solution of the given system of equations help of…

Q: You want to find the Fourier series for the funtion tan(x) over the interval -2π to 2π. Will the…

A: Follow the procedure given below.

Q: Use the graph to locate the absolute extrema (if they exist) of the function on the given interval.…

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Q: A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = 6t² – 24t +…

A: Given : vt=6t2-24t+18 we know that when particle is moving to right v(t) > 0

Q: Let f(x)=-4x-1 and g(x)=x²-2 Find f(g(6)). f(g(6)) -

A: Please see the below picture for detailed solution.

Q: 3. (a) Find the Laplace transform of (i) f(t)=17te-2-3 sin(9t) (ii) fo

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Exercise 11 = (ƒ(x) + 5.x²)4 Let y = The Chain Rule and suppose that f(-1) = -4 and dy = 3 when…

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Q: Suppose y = √ 2x + 1, where x and y are functions of t. dx (a) If = 12, find dt dy dt dy (b) If = 3,…

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Q: Set up, but do not evaluate, an integral for the length of the curve. x = 7 sin(y), osys. 1. (C dy 2

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Q: XYZ Things Inc. produces and sells pressure washers per year at $p per pressure washer. The demand…

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Q: A particle moves along the x-axis so that its position at time 0 < t < 18 is given by x(t), whose…

A: Here position of particle represents by xt Then x't is velocity/speed of particle  so particle speed…

Q: The Chain Rule Exercise 8 y = (3.x²+1)³: (a) Decompose the function in the form y = f(u) and u =…

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