Show that: l (i) a a a a al la al = = (2a +l)(l

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

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Q: 1. f(x) = 3ex +1 2. f(x) = 45x + x45 3. f(x) = 10 sin x + 5 sec x 4. f(x) = x²(2x + 1)

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: [ (ax + b) c+b) dx = ○ / (ax + b) ² + C O O4a ¹ª (ax + b) ² + C O4a (ax + b)² + C O4 (ax + b) + C 7a

A: You must have basic idea about indefinite integral in order to understand this better.

Q: 15. Use the results of problems 12,13 and 14 and assume that the Maclaurin Series expansion for ex…

A: We have to prove the given equation of complex number

Q: Consider the following. [u-5(6 - u³ +4²0) du Simplify the integrand by distributing u¯5 to each…

A: We know that integration power rule is given as - Integration of xn is xn+1/n+1 +C ; here C is…

Q: P3: Calculate the volume of solid of revolution when the region bounded by y = cos x and x² - y - 2…

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Q: The diversity of a population that contains two species can be measured by the Gini-Simpson…

A: The diversity is given by H(p)  H(p) = 2p(1-p)   H'(p) = d/dp(2p(1-p)) H'(p) = 2(1-p) -2p H'(p) =…

Q: P2: Calculate the volume of solid of revolution when the region bounded by y = √x + 4 and x - 2y + 4…

A: Given problem:- Calculate the volume of solid of revolution when the region bounded by y = √(x + 4)…

Q: Find the area moment of inertia with respect to x of the plane region y=9-x^2 bounded by the…

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Q: Find the area of the largest rectangle that can be inscribed in a circle of radius 20 cm. Answer:…

A: Find area of largest rectangle that can be inscribed in a circle.of radius 20cm

Q: 8 The angle between 0 and 27 in radians that is coterminal with the angle -π in radians is 3

A: The answer is given below:

Q: integrate using partial decomposition (y^2)/(y+1)(y-1)

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Q: Consider a plate (the plate has the same shape as the region enclosed by y = x² and y = 4) submerged…

A: Let's find force(F).

Q: 10- There is a rectangular playing field in Alaska Denali Park for a grizzly Bear with an area of…

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Q: x3 5x² Find the absolute maximum and absolute minimum of the function f(x) = + 4x + 2 over the…

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Q: Find F(s). ℒ{t3e−4t}

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Q: Find the integration of the following functions COSX 1) dx 3+8sinx 2) fx tan(x² + 1)dx

A: In this question, we want to solve the given integrals.

Q: f arctan y dy 3 f

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Q: 1 dx 49 1 42 49 arcsin 7x) - 49 sin 2 arcsin 7x+C (2x) 2 (1 x)) X

A: Given, ∫ x249-x2dx

Q: 1- Calculate the area of the region which is bounded by: y = (x - 1)², y = (x-4)2, and y = 0.

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Q: (c) Use the WASHER METHOD to set up a (sum of) definite integral(s) that is equal to the volume of…

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Q: For the function whose graph is shown below, at which value of x is the graph continuous and…

A: We know  Function differentiable if it is continuous through out its domain   At sharp/corner points…

Q: For the following integral, reverse the order of integration and evaluate the integral. 1/8 1/2 S S…

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Q: Deriving the formula for volume generated by revolving the first- 8x and the line x = 2 about =…

A: Given problem:- Deriving the formula for volume generated by revolving the first quadrant area…

Q: The function f(x) 2x³ + 42x² = one local minimum and one local maximum. This function has a local…

A: You must have an idea how to use derivatives to find the local maximum and minimum using critical…

Q: The volume generated by revolving about the y-axis the area bounded = 0 and y = 16. by the curve y =…

A: Volume is evaluated.

Q: se the Shell Method to compute the volume of the solid obtained by rotating the region above the…

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Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

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Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

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Q: Given: y² = 2x - 2 bounded by y = x-5. The points of intersection of these two curves are {A}…

A: y2=2x-2 bounded by y=x-5

Q: 4- Find the volume of the solid obtained by rotating about the x-axis the region under the curve y =…

A: Given curve, y=5x from 0 to 4

Q: C

A:

Q: Use the Laplace transform to solve the given initial-value problem. y'' + 2y' + y = 0,  y(0) = 1,…

A: A detailed solution is given below.

Q: f(x) = 4x5 (12x² + 15x + 3)

A:

Q: Differentiate the function with respect to the independent variable. f(x)=-7x+5x³-6 f(x) =

A: Given, f(x)=-7x4+5x3-6

Q: Find the average rate of change of from y = x³ - 2x + 3 from 0 to x = 3. -

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Q: What function do you know from calculus is such that its first derivative is itself? (Do not use the…

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Q: Differentiate g(N) = rN g'(N)= with respect to N. Assume that K and r are positive constants.

A: We need to find g'(N).

Q: tody + y² = 0 dt

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Q: dy ({})y+3

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Q: Find the arclength of the curve y = 3x² + 5 on [0,3].

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Q: Consider the following. y = = In(x²) Find y'. y' = Find the slope m of the tangent line to the graph…

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Q: 19. Find x from the following equations: 27x = 9y 81*3-* = 243 A. 2.5 B. 2 C. 1 D. 1.5

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1)y= (8+7x³) Find the derivative of the following functions 2)y = (x +5)®(2x + 3) 3)y=

A: We have to find the derivative of the given function

Q: Consider the utility of a consumer consuming two goods, the quantities of which are x and y. His…

A: Let's solve.

Q: ƒ(5x² + 4x³ − 2x + 1)dx 이름 +2 -를 +a + C 5 2 O x5 x5 + x²-x²+x+C O 20x5 + A O 20x³ + 12x² −2+ C…

A: Given, ∫(5x4+4x3-2x+1)dx

Q: The height​ (feet) of a ball launched in the air t seconds after it is launched is given​ by:…

A: The height​ (feet) of a ball launched in the air t seconds after it is launched is given​ by:…

Q: A giant spherical-shaped snowball is melting. If the radius decreases at the rate of 0.5 in/min, now…

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Q: 21

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Q: Solve the following equations 2)3x+2 = 27 1) 2Ln(√x + 3) + 2Ln(√x-1)=Ln(6x-7) I 1 1

A: Let's solve both equation.