The value of the following limit is -1 None Undefined 0 1 +∞ fin(n+¹) coth x dx limn→+∞ Jin n

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A: We have to find the rate of change of cost, revenue and profit.

Q: write the cubic polynomial function f(x) in expanded form with zeros -4, -1, and 3, given that…

A: given zeros  -4,-1 and 3standerd form is  f(x)=a(x+4)(x+1)(x-3)given   f(2)=20

Q: Find the equations of the tangent and normal to x² - y² = 7 at the point (4, -3).

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Q: Consider J₁ x²y dA, where R is the region bounded by 0 ≤ x ≤ 2, x ≤ y ≤x+4. R

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

A: given f''(x) =4x2

Q: 1. Find the exact value of the iterated integral: 11₁ If sin(x²)dxdy 0 y

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Q: (c) Let F(x, y, z) = x^3i + y^3j + z^3 k i) ∇ · F (ii) ∇ × F

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A: Let's find the value of W.

Q: mange the point (-2,2, from rectangular to cylindrical coordinates and spherical coordinates. √²-25²…

A: Given ;  Point = (-2,2,1).

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A:

Q: Using Rolle's theorem for the following function, find all values c in the given interval where…

A: Given query is to apply rolle's theorem.

Q: Show that Rolle's Theorem can be applied to the following functions on the closed interval [a,b],…

A: According to Rolle's theorem , if a function f is continuous on the closed interval [a, b]…

Q: 1. Obtain the general solution by the indicated technique: separation of variables 1.1…

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

Q: 3 2x S 2 (1-x)² -dx

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Q: Write each equation in polar coordinates. Express as a function of t. Assume that r > 0. (C) x² + y²…

A: NOTE: Refresh your page if you can't see any equations. . use the cartesian to polar substitution…

Q: Question Three (a) Prove that F(x, y, z)= (y² cosa+z³)i+(2y sin a-4)j+(3rz+2)k is a conservative…

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Q: f(x) = x³ − 15x² +27x2. F

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Q: termine the intervals on which f is increasing or decreasing, assuming the figure below is graph of…

A: Given query is to find the interval where function increasing and decreasing

Q: Find an equation of the tangent plane to the surface z = 2y² – 5x² at the point (2, 0, -20). Z

A: NOTE: Refresh your page if you can't see any equations. .

Q: Convert to a logarithmic equation. Gf=A

A: lnxn=nlnxlnab=lna-lnbgiven  Gf=A

Q: 1. Consider the graph of the function f below. I -4 -3 42 1 5 4 3 2 -1 -2 -5 Y I 1 y = f(x) I I 3 Т…

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Q: Let G₁ be the solid in the first octant that is inside the paraboloid 2x² + 2y² = 8-z and below the…

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Q: f sec³3xcos3xdx

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Q: Evaluate the integral. -π/4 JO 5 sec(0) tan(0) de

A: To evaluate the following integral.∫0π4 5 secθ tanθ dθ

Q: (a) What is the difference between a sequence and a series? A sequence is an ordered list of numbers…

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Q: 1. Chapter 14 Review 57: Find the minimum and maximum values of f(x, y) = x²y on the ellipse 4x²…

A: To find the minimum and maximum values of fx, y=x2y on the ellipse 4x2+9y2=36.

Q: Consider the system below. y = kx2 y' = k'x2 + 2xv y" = k"x2 + 4xv' + 2v Now, find y' and y"…

A: We need to find y' and y''

Q: or a certain company, the cost for producing z items is 55x + 300 and the revenue for selling z ems…

A: Given query is to find the profit function and the value of x when profit is $50.

Q: Evaluate lo Vf. dr, where f(x, y) = x² ln(y) and C is any curve from (8, 1) to (13, e).

A: The answer is given below: Topic: Line integral

Q: Problem 7. Write the first six terms of the sequence. Then, describe the trend of the terms of the…

A: we need to find out the first 6 terms and its limit.

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, P4(x) = c = 7

A:

Q: A projectile is launched into the air. The function h(t) = -16 + 32t + 128 gives the height, h, in…

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Q: Find the slope passing through the two given points. 1.) (1,-3) and (0,1)

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Q: (a) A water container, whose circular cross section is 6 ft in diameter and whose height is 8 ft, is…

A: Given:    A = area of the tank a = area of bottom hole…

Q: Given f(x) = 6x + 3x, find intervals of concavity and the x-coordinate of any inflection points.

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Q: Use the graph of the function to estimate the interval on which the function is increasing. y -SA-…

A: Increasing Function:  If f(x) is a function, and x1 and x2 are any points in the domain such that x1…

Q: Find the minimum and maximum values of the function f(x, y) = x2y4 subject to the constraint x2 - y²…

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Q: 6. Determine the domain and range of the vector valued fun r(t) = (In(t-2). √²) 1 t-4' fang

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Q: Find and classify the stationary points of f(x, y) = (x² + y)e/2.

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Q: = x³ +. 5. f(x) = 忘 3x = y + 4 = U x + 2y 6=0

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Q: d dx tan x S 2 2 1 + tdt

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Q: ) Obtain the differential equation of the family of plane curve described and sketch at least 5…

A: We have to find the differential equation of the family of plane curves, that is "straight lines…

Q: Evaluate the limit: lim, +∞ (e² + x) =

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Q: Determine the vertex, pocus, directrix and axis of symmetry of the parabola with the given equation.…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 1. ) Obtain the differential equation of the family of plane curve described and sketch at least 5…

A: We know slope intercept form of line ⇒y=mx+c

Q: Chapter 14 Review 57: Find the minimum and maximum values of f(x, y) = x²y on the ellipse 4x² +9y² =…

A: Given function:- fx,y=x2y Let gx,y=4x2+9y2-36

Q: If f(x) = (3x -5)e-2x , find f'' (x)+ 4f' (x) + 4f(x)

A: To determine the given value with derivatives and function

Q: Use polar coordinates to find the volume of the solid bounded by the parabolas z = 3x² + 3y² and z =…

A: The solid is bounded by the curves:z=3x2+3y2        and          z=4-x2-y2

Q: Find the differential equation by eliminating the arbitrary y = Asin 5x + B cos 5x constant State…

A: we need to write down the differential equation by eliminating the arbitrary constant.