Consider the following series. n = 1 Use the Limit Comparison Test to complete the limit. n 1 1 n° + 3 8 n° + 3

Q: 67. Let f(x)=√x³ +1. o fº√x² S a. Find a Midpoint Rule approximation to b. Calculate f "(x). x³ + 1…

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Q: Suppose f(x) = xe-³x, 0≤x≤ 2. Use the Closed Interval Method to find points at which the absolute…

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Q: J sin’rVcos ad

A: Here is the solution:

Q: y-axis. find the area of the surface obtained by rotating the curve about the y = x², 0≤x≤ 2 y=x+1,…

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Q: Find a function f(x) such that f'(x) = 7e² + 4x and f(0) = −2 f(x) =

A: We need to find out the function.

Q: Drum Tight Containers is designing an open-top, square-based, rectangular box that will have a…

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Q: Find the following for the function f(x) = 3x² + 4x -2. (b) f(1) (a) f(0) (e) - f(x) (f) f(x+3) (a)…

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Q: Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a shape…

A: Given Data: The rate of volume of gravel dumped is: dVdt=10ft3/min The relation between the base…

Q: Given the equation for a “tilted” ellipse: x^2-xy+y^2=3 . Find the points (x, y) on this ellipse…

A: Here we have to find the largest and smallest values of x.

Q: Determine the number that should be added to complete the square of the expression. Then factor the…

A: given  x2+16x

Q: Determine the absolute extreme values of the function the interval 0≤x≤2л. f(x) = 2 cos x - Con

A: Whenever we find the extreme values ofthe function y=f(x) in the interval [a,b] then we apply the…

Q: By considering different paths of approach, show that the function below has no limit as (x,y) →…

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Q: J x √16x² zdx

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Q: Consider f(x) = (a) f'(x)= = x² -1x - 78 x+6 (b) Find all points P(x, y) on the curve y = f(x) whose…

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Q: Strength of a Beam A wooden beam has a rectangular cross section of height h in. and width w in.…

A: We use optimisation techniques using differentiation to find the required dimensions. The answer is…

Q: Given an acceleration vector, initial velocity (uo.Vo,wo), and initial position (Xo YoZo), find the…

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Q: Assume C is a circle centered at the origin, oriented counterclockwise, that encloses disk R in the…

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Q: Find the absolute maximum and minimum of f(x, y) = 2x + 4y within the domain x² + y² ≤ 25. Please…

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Q: Find all the second-order partial derivatives of the following function. h(x,y) = 8xey + 6y + 4 0-4…

A: h(x,y)=8xey+6y+4∂ex∂x=ex∂xn∂x=nxn-1∂ ∂x(constant)=0

Q: Calculate the integral, if it converges. If it diverges, enter diverges for So e dx = your answer.

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Q: АМАИ 4. In the system below, k is a constant and x and y are variables. For which value of k will…

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Q: Evaluate the integral by making a u-substitution and then integrating by parts. ENOTE: Enter the…

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Q: Graph f(x) = 5, x = 3. ind lim f(x) and lim f(x). x→3 x→3* oes lim f(x) exist? If so, what is it? If…

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Q: 20 Let f(x) = 3x + Then the equation of the tangent line to the graph of f(x) at the point (2,11) is…

A: The given function is fx=3x+20x2 and the point is 2,11.   The objective is to find the equation of…

Q: Find the area of the surface S, where S is the surface given by r(u, v) = (u cos v)i + (u sin v)j +…

A: Given Surface equation:- r→u,v=ucosvi→+usinvj→+uk→

Q: The plane containing the point (0,-1,-8) and parallel to the plane 3x - 6y + 2z = -2 has equation…

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Q: Evaluate (2x + y)ds, where C is the line segment from (0,2) so (3,-2), i.e., C: r(t) = (3t, 24t), 0…

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Q: Finn all local and global maxima and minima for the function f(x) = 2x3-3x + 2 in the interval [-1,…

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Q: Find the line integral of F= √√zi-2xj + √yk, from (0,0,0) to (1,1,1) over each of the following…

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Q: The graph of y = f(x) (solid) and y = g(x) (dashed) is shown -6 -5 4 -3 f(x) lim 2-1 9(2) -∞ 00 8…

A: The given graph is:

Q: line to the graph of y = g(x) at x = 4 is 4x+12y = -56 It follows that y = is the equation of the…

A: Given that at x=4, 4x+12y=-56 is a tangent.

Q: Labs Find the minimum cost of a rectangular box of volume 100 cm³ whose top and bottom cost 4 cents…

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Q: 8. Draw a right triangle (with labeled sides) representing the angle (cot-¹(x/2)) and find sin(cot…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Explain how you would prove if four given points are coplanar. Use the method you described to…

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Q: Give the derivative formula for the function. f(x) =  6x2−3                 3x

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Q: dr Let A be the area of a circle with radius r. If dt = 3, find = dA dt when r = 4.

A: Area of circle having radius 'r'  = πr2  Chain rule of differentiation :  dydx= dydu× dudx Power…

Q: Find the following limit. 25√√x - √√x 3³√√x +3¹/√x lim X→ ∞ 3 lim x→∞ 2³√x - √√x 5 3√x + 3√x 11 co…

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Q: The slope of the tangent line to the parabola y = 3x² + 2x + 5 at the point (1, 10) is: The equation…

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Q: Find and sketch the level curves f(x,y) = c on the same set of coordinate axes for the given values…

A: This is a question of curve plotting of the function for different value of c. Given equation is of…

Q: Minimize Q = 4x^2 + 3y^2 where x + y =7

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Q: f(x) = cos(√x) + 2 The slope of the tangent line to the curve y = f(x) at the point where x = 4 is A…

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Q: At what points is the function y = x+8 2 x-15x + 56 continuous? Describe the set of x-values where…

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Q: at satisfy the conclusion of the Mean Value Theorem for the following function and interval. Enter…

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Q: Find the solution of the following initial value problem. = 9x (x² - 1); g'(x) = 9x xo The solution…

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Q: lim f(x) = L and lim f(x) = M, where L and M are finite real numbers, then how are L and M related…

A: Given query is to find relationship between L and M.

Q: it exists) integral (if it exists) Find the indicated integral (if ·∞ e4x e8x + 1 dx =

A: The given integral is e4x/[e8x+1], limit from -infinity to infinity.

Q: Find the tangentline and normal line for the point (-1, 0) for the curve given the function y3 cosh…

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Q: A rotating light is located 20 feet from a wall. The light completes one rotation every 4 seconds.…

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Q: We know how to determine if a given table with x and y represents a function of x or not. In this…

A: x is a function of y    here we find value of c by equating two values at same point

Q: Question 4 For the integral: Write the integral again as: 0 0 x+2y+1 --LIT- V = -1 -(x+1) ? ? ? v =…

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