Let R be the region bounded by the following curves. Find the volume of the solid generated when R is revolved about the y-axis. y = , y=0, x=4 Set up the integral that gives the volume of the solid. dy 0 (Type exact answers.)

Q: - 1 Find y' for y=7x7 + 9x¯ y' =

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A: Given :dy=2e3xdx

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A: Given function, f(x)=4x2+16x+12x+3

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Q: Solve the given differential equation 5x4cos 2 ydx - dy = 0 (A) y = tan-¹ (x5 + C) B) y=x5+ C C y =…

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A: The given function is fx=π We have to find the derivative of fx

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Q: 2x 2-3+ x - 3 Example 9. Find lim 2x x-3-x-3 and lim

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Q: Consider the following. f(x)=x²-6x² + 7

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Q: Find the inverse of the following functions. Determine the domain and range of both the function and…

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Q: Examples: Use the first part of the Fundamental Theorem of Calculus to find the derivatives. tanx 5.…

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Q: Find an expression for the inverse of f(x) = e³x+1. f-¹(x) = 4

A: Topic- functions and inverse functions We are given, f(x)=e3x+1 we know that ln(ex)=x

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Q: Solve the differential equations. 3. dl dt + KT-100k,

A: The solution of the given differential equation is as follow.

Q: Problem #6: Evaluate the following by changing to polar coordinates. .3 √49-2 1 So 22-²3-2²-32 dx dy…

A: Given:- ∫03∫9-y249-y213+x2+y2dxdy+∫37∫049-y213+x2+y2dxdy

Q: D(t)=-1560+49(t) After how many hours does the submarine reach the surface? Give your answer as a…

A: The objective of the question is determine the time take by submarine to reach to the surface.

Q: Prove, using the formal limit definition of the derivative, that if f(x) = then f'(3) = - 1-2x x3 s…

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Q: Find the curvature of the curve r(t) = (-2+5 cost, -1, - 3 - 5 sin t) at the point t = A|CO 3 ㅠ.

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Q: Q23&Q27 As these are very easy questions so solve both questions in the order to get positive…

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Q: ONLY DO THE GRAPHS AND EMPHASIZE THE LIMITS 1. 2. 3. x²-25 lim 10 x²4x-5 x²-25 lim z+5 x² - 4x-5…

A: 1. Given limit  limx→0x2−25x2−4x−5 The graph of the function is given below : Here, we can see that…

Q: Solve the differential equation. 3y" + 29y' + 56y = 0 Ay=c₁e7x + c₂e-8x/3 B) y=c₁e-7x + c₂e³x/3…

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Q: For f(x)=5x-1 and g(x)=x+1/5 find the following function (fog)(x)

A: given that f(x)=5x-1 and g(x)=x+15 find (fog)(x)?

Q: S dx 2 (1+x²)²

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Q: Compute the derivatives of the given functions. a)  f(x)=ln(7x5)  f′(x)= ___ b) g(x)=ln(4√x,…

A: This is a problem of derivative. Please follow the procedure given below.

Q: Find the domain and range of the function. f(x) = 3+x² Identify the domain of f(x). (Type your…

A: Given, f(x)=3+x2 Aim: Find Domain and Range

Q: Solve the differential equation. 2x dy + y dx = 9x5 dx 9 A y 2x11/2+cFx By = 9x5 + c)y= X4+ D)y= 9…

A: Here is the solution:

Q: Find the profit function if cost and revenue are given by C(x) = 178 +6.1x and R(x) = 9x -0.02x².…

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Q: 26. A cylindrical can has volume 355 cc. (cm³). If the bottom and sides cost 2cents/cm² while the…

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Q: 1. 2. x²-25 lim 1-0 ²-4x-5 x²-25 lim 15 x² - 4x-5 7x²-4x-3 r+1 3x² - 4x + 1 3. lim

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Q: 1. Para la serie de potencias E-01 determina (x+4)" n=0 115 a. El centro b. El radio de convergencia…

A: See this solution in below.

Q: Use the Generalized Power Rule to find the derivative of the function. f(x) = F(x)=(x²+1)

A: As we know from the Generalized Power Rule: ddxfxn=nfxn-1·ddxfx The Sum/Difference Rule: f±g'=f'±g'…

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Q: None of these anwers were right

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Q: b) Assume that the function is exponential. Complete the rest of the table. 1. II. T III. X 1 2 3 4…

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Q: Experiments show that a colony of bacteria with sufficient food and no predators and with zero death…

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Q: Problem #2: Evaluate Sfxy ex²164, R where R = {(x,y) | 0 ≤ x ≤ 2, 0 ≤ y ≤ 8}. dA,

A: For the region R , limit of x is x=0 to x=2limit of y is y=0 to y=8

Q: 1. Discuss the monotonicity (i.e. identify the intervals of x over which the function is increasing…

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

Q: For f(x)=5x-1 and g(x)=x+1/5 find the following function (gof)(x) IF

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Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: Topic-Limits We are given,f(x)=9-3xifx<3x2-xifx≥3Limit exists at x=c if limx→c-f(x)=limx→c+f(x)if…

Q: Solve the differential equation. 6y¹ = ex/6 + y A) y = B) y= xex/6 + cex/6 6 D) y = XEX/6+2 6 Ⓒ y =…

A: Solution of the given differential equation is as follow

Q: find scalars c1, c2, and c3 for which the equation is satisfied. 19. c1(1, −1, 0) + c2(3, 2,…

A: Given,  c1(1, −1, 0) + c2(3, 2, 1) + c3(0, 1, 4) = (−1, 1, 19) That is  C1(i-j) + C2(3i+2j+k) +…

Q: Find the fourth derivative of f(x)=3x^−2

A: As we know that ddxxm=mxm-1see below the calculation and answer

Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 14…

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

Q: Solve the differential equation. dy + 5y dx = e-5x dx A) y = 5x + ce-5x B) y = e-5x (x + c) (C)…

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