Find the inverse of f(r) = log, (3z + 1) +2 %3D

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 – 2xy + y?,…

A: Solving tangent equation

Q: 1 1 (1++)dr

A: To Evaluate: ∫121+1x+1x2dx     Note : ∫1xdx=logx+C∫xndx=xn+1n+1+C

Q: The solid of revolution is obtained by rotating the region bounded by y = x² – 2x and y = x about…

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

Q: Using Laplace transforms. Solve y" + 4y′ + 3y = e^t. When, y(0) = 0 and y′(0) = 0. Whole Solution

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Q: In the year 2000, the population of a small city was 42,000. The population grows at a rate of r(t)…

A: Given: r(t)=1200e0.04t

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A: We will find minima, maxima or saddle point.

Q: Use the graph mate the open intervais on whichn the function is increasing or decreasing. Tnen find…

A: Consider the function  y=-x+22

Q: V8x 1. S V³ ++ dx V4x2

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Q: Let the region be bounded by the curves y= 2 /x and y = 4, and x 16. i) (ODraw this bounded region…

A: Given problem:- Let the region be bounded by the curves y = 2√x and y=4, and x = 16   i) Draw this…

Q: The marginal cost for a company to produce q items is given by MC(q) = 0.003q - 0.5q + 620. The…

A: Given: Marginal cost for a company to produce q items: MC(q) = 0.003q2 - 0.5q + 620 Company's cost =…

Q: Find the Fourier series expansion of the periodic ʻramp' function f(x)= 2x, valid between x = 0 and…

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Q: Y = Vx + 30 y = x Y y = 0

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Q: company produces a spherical object of radius 23 centimeters. A hole of radius 5 centimeters if…

A: We

Q: In practical applications the Richter magnitude depends on local geological factors and the aver…

A: The given reasonable model is R(A)=logA2.5+4.25 .............................. (1)

Q: Find the gradient of the function at the given point. g(x, y) = 3xe/x, (10, 0) Vg(10, 0) = 3i + 3i

A: g(x, y)= 3 x eyx∇g(x, y) =∂g∂x, ∂g∂y∂g∂x=3eyx+3x eyx-yx2      =3eyx 1-yx∂g∂x=3eyx (x-yx)∂g∂y=3x1x…

Q: x – sin 2x -dx x + cos2x

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Q: Use the First Derivative Test to find the local maximum and minimum values of the function. y = 2x2…

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Q: Problem #6: Consider the following function. H(x, y) = 7 In(3x² +y³) %3D (a) Find f(2,3). (b) Find…

A: a. fxx(2,3)  = 42(-3×22+32)(3×22+32)2fxx(2,3)  = -0.2857

Q: 3) "s) Determine the highest real root of f(x) = 3x' +11,8x -17,8x-6 a) Graphically,

A: f(x)=3x3+11.8x2-17.8x-6from below graph, highest real root is x= 1.386

Q: Hazel is 24 and wants to retire at age 62. She deposits $1,100 at the end of every 6 months into a…

A: We have to find how much money does she have in the fund when she retires, size of the monthly…

Q: Use a definite integral to find the area under the curve between the given x-values. f(x) = ex/7…

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Q: Find D in the partial fraction decompositon 12x2 -8x+40 Cx+D + x² +9 B (x-4)(x2 +9) X-4 O 9 O 7 O 10…

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Q: Using separation of variables, solve the differential equation, dy e sec(x) – -cos(x) = 0. dx Use C…

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Q: 2r –1 15. Evaluate dx. (x– 2)(x+1)' A) hx- 2| + hịx + 1| +C C) -hx – 2| + Inx + 1|+C B) hx- 2| – hịx…

A: To evaluate: ∫2x-1(x-2)(x+1)dx

Q: Solve the initial value problem. dy 2xy = 8x, у(0) — 0 dx y =

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Q: f(x) = e-=/2; [-1,2]

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Q: onsider the following function. f(x) = x2 - 8x (a) Find the critical numbers of f. (Enter your…

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Q: nitial ter t und?

A: The distance s from the ground is given by;s(t)=96+80t-16t2When, ball touches the…

Q: -(-3у?-у-2)dy 2y3+y2+4y

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Q: 10x – 2 - dx . (x + 1)(5x² – 2x + 1) 16. Evaluate 5x - A) hx +1|+ n|5x² – 2x + 1|– tan +C 5x- B) Inx…

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Q: Show that the signum function is discontinuous at x = 0

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Q: Evaluate the integral. 8. 9. dx x² 7.

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Q: Preview Activity 1.1.1. Suppose that the height s of a ball at time t (in seconds) is given in feet…

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Q: Demand for a certain kind of SUV obeys the following equation, D(x, y) = 21,000 –Vx – 13(0.9y –…

A: Here, the given function of demand is: D(x,y)=21000-12x-13(0.9y-10)32 where x is the price per car…

Q: (3x²+vx)dx 3. 5 2x3 r2-12

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Q: can you please check my answer? Thank you.

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Q: Solve D.E using bernouliis equation r'y-x'. dy x'y-x' . dx = y* · cos(x)

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Q: Find the area of the region that lies inside the curve r = 10 cos 0 and outside the curve r = 5,…

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Q: To determine the volume of the solid obtained by revolving the region bounded by y = Vx, y = 3 and…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the absolute maximum and minimum of the function f(x,y) = 4y² + 18x – 18 over the closed region…

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Q: Σ Use the Direct Comparisơn Test to determine the convergence or divergence of the series. 00 1 Σ…

A: I have appended the formula used in the solution part.

Q: Evaluate the integral of the volume of the solid formed by revolving the region bounded by x² + y =…

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Q: Find the point of diminishing returns (x,y) for the function R(x), where R(x) represents revenue (in…

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Q: has 1100 ft of fencing to fence in a rectangular horse corral. 550- x (a) Find a function that…

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Q: (5) Consider the several variable function f(x, y, z) = xe²y + yeš + ze¬². Give a general formula…

A: The given function,   fx,y,z=xe2y+ye3z+ze-x

Q: Consider the curve given by the following: r = 4 cos (0),0 < 0 < n . Find the values of 0 such that:…

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Q: Evaluate the integral 1 12 3x (x - 1) dx 0.

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Q: Find the Taylor series expansion for the following function about c = 4: f(x) = Vx

A: Taylor series of function fx at c is defined as:fx=fc+f'c1!x-c+f''c2!x-c2+f'''c3!x-c3+…

Q: Preview Activity 1.1.1. Suppose that the height s of a ball at time t (in seconds) is given in feet…

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Q: 1 let w = f(x, y, z) = Vx²y+y² z+z²x and x = 3st, y = 4st, z = 2st. a) Find ow dx dw b) Find dt and…

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