Use the comparison test to test the series i n²-1 n = 1 n* 4

Q: y" +y = 0, y(7/3) = 2, y(T/3) = -4. = -4.

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Q: OR = {(r, 0): 0 <r< 6 cos(30), 0 < 0 < n}

A: Follow the procedure given below.

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

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Q: Find the arc length of the graph of r(t) = ev2ti + e¯v2tj+ 2tk, 0<t< v2 In 6 NOTE: Enter the exact…

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Q: f(x)=x+ 1. Donain 2. Intercepts (y-only) 3.Any Symmetry 4. Cvitical Paints 5. Intervals ok…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 4. S tan x dx CSC X sec (In x) dx 5. dx 6. S; 1- cos 2x

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Q: Set up and evaluate the integral for finding the area and moments about the x- and y-axes for the…

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Q: Consider the differential equation y = yz+2z a) Use Euler's Method to estimate y(z) on (0, 1] using…

A: Given :y'=y2x+2xBy Euler's formula :yn+1=yn+h(xn+yn)We know that  y(0)=0, So, x=0 , y=0 and…

Q: What is the minimum product you can achieve from two real numbers, if one of them is three less than…

A: This question is based on application of derivative.

Q: Find all the relative and absolute extrema of the given function on the largest possible domain.…

A: Given,  g(x)=(x-6)2/3

Q: (c) Find a and b such that the following function is continuous at z= 1: (2² + a, z1.

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Q: Use the shell method to set up and evaluate the integral that gives the volume of the solid…

A: Let gy be continuous and nonnegative, then, the volume of the solid of revolution formed by…

Q: Integrate: 2x +3_ dx' 1. dx (2x "5)(xt5) 2.

A: A detailed solution is given below

Q: 4. An object is moving along a horizontal line according to the position function s(t) = 2t - 21t? +…

A: Let's find.

Q: Question 2 Let f: (ry. ry) and g:= (cos(t), sin(t)). Then determine the following. (a) fog.

A: This is a problem related to combined function. Based on the general concepts and formula we will…

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: S sin x (1+ cos x) ecos *dx 2. S csc ³ () do 1.

A: 1) Given:       ∫sinx1+cosxecosx dx Integrate by parts:         ∫fg′=fg-∫f′g here  f=1+cosx→f'=-sinx…

Q: 3x3/2 2е + dx

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Q: Consider the following optimization problem. Maximize P = xyz with x + y = 36 and y + z = 36, and x,…

A: We have to find P(y), P'(y) and maximize P.

Q: ꭍkg(x)dx=___ where k is a constant * a.(k/2)ꭍg(x)dx b. ꭍg(x) c. kꭍg(x)dx d.1

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Q: Solve the following dy x. ey, +y. e*y - 4x3 = 0 dx 3.

A: A detailed solution is given below

Q: (a) Suppose that f is differentiable, positive and decreasing on (a, b] and has no critical points.…

A: Given problem:-

Q: The following figure shows the graphs of y = f(x) and y = g(x), together with the indicated areas. C…

A: to

Q: that has i +j and i – 18j as adjacent sides. NOTE: Enter the exact answers. ||d||= 19 ||d||=|17.12

A: Vector

Q: Find u · v, u· u, ||v||², (u · v)v, and u · (3v). u = (3, -2, 5), v = (0, 7, 4) (a) u. v (b) u.u (c)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: A water tank in the form of an inverted cone is being emptied at the rate of 5 m3/min. The height of…

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Q: Given that f(x, y) = 8x-2x² - y² +8y with the constraint g(x,y): 2x+y=5. Determine the optimum value…

A: Solution is given below:

Q: 4. A particle moves in a straight line and has acceleration given by a(t) = 6t + 4. Its initial…

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Q: II. MULTIPLE CHOICE. Read and analyze the questions then write the letter that corresponds to your…

A: As per our guideline we supposed to answer only the first three question

Q: plve the following related rates and optimization problems. We want to build a greenhouse that has a…

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Q: Solve the Differential Equation using the substitution suggested by the equation

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Q: 7. x Arcsec (2x) dx (4x² – 1)7

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Q: g. There is a removable discontinuity at = 1 and f(1) = 4 h. There is a jump discontinuity at z = 2…

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Q: Question Find the absolute maximum and absolute minimum of the function f(x) = = - 2r² + 4 over the…

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Q: A product is introduced to the market. The weekly profit (in dollars) of that product decays…

A: A product is introduced to the market. The weekly profit in dollars of that product decays…

Q: Find u · v, u · u, ||v||2, (u · v)v, and u · (3v). u = (3, -2, 5), v = (0, 7, 4) (a) u: v (b) u: u…

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Q: 2x e3a² dx

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Q: Determine the maximum and minimum values ​

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Q: Q1/ a) Sketch the graph of y = sin2x for 0 <x SI %3D b) find the total area bounded by the curve and…

A: This is a problem related to calculating area under curve of the polar equation. Based on the…

Q: C. Given that log, 2 = 0.693, log, 3 1.099, and log, 5 1.609, find each of the following, if…

A: Given that,  logb2≈0.693, logb3≈1.099, logb5≈1.609 We need to find the value of each of the below…

Q: 4. A particle moves in a straight line and has acceleration given by a(t) Its initial velocity is…

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Q: x^n dx=x^(n+1)/(n+1)+C is not possible when    a. n=0   b. n=1   c. n=-1   d. n=2

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y…

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Q: rector-valued function. (Enter your answer using interval not :), where F(t) = cos ti – sin tj +…

A: We have to find the domain of the given vector valued function

Q: The elasticity of a polymer is affected by the concentration of a reactant. When low concentration…

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Q: 3. In the differential equation (2x+ ydx-3(2x + y+4)dy =0, we let the substitution dy :

A: We can solve the given differential equation  by  using  the substitution            u = 2x+y

Q: Find the volume of the solid formed by revolving the region bounded by y = x – x and the x-axis (0 <…

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Q: Find the solutions of the system of inequalities by graphing: 2x – y 0

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Q: 5. Find the indefinite integral. a) S 2*-+52 dr b) S Va(zi - a² +z)dx b) S Va(a – a² +r-)da c) S…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Consider the following. u = (-2, 5, 4) v = (0, 1, 7) %3D Find u x v. Determine if u x v is…

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