(a) Ratio Test: (n+1)! n=0 n+2 (b) Ratio Test: 51-n (n+ 1) n=1 5n2 – 2n +1 3n2 +n – 3 (c) Root Test:). n=2

Q: Let C = (1,–3, 2) and D = (-1, 2, – 3, ). Find the following. (a) The cosine of the angle between D…

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Q: Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x) = - 2…

A: This is a problem related to function calculation. Based on the graph we can find out the interval…

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Q: Find r'(t), r'"(t), and r'(t) · r"(E). r(t) = (t2 + 7t)i – 2t?j (a) r'(t) (b) r"(t) (c) r'(t) ·…

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Q: 13 For the sequence an = n +1' its first term is its second term is its third term is its fourth…

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Q: Choose the rule that you would use to most efficiently find the derivative of the function. f(x) =…

A: Given f(x) = 8√x^3

Q: Find the radius of convergence, R, of the series. (x + 6)" 6" n = 1 R = Find the interval, I, of…

A: Consider the power series           ∑n=1 ∞ an(x-a)n then , series convergent if x-a<R , where , R…

Q: 1. Solve the following quadratic equation by completing the square: x2 – 6x +4 = 0

A: We are authorized to answer one question at a time , since you have not mentioned which question you…

Q: Find an equation of the plane that passes through the points (-2, 1, 1), (0, 4, 7), and (1,0, –1).…

A: The plane that passes through the point,       -2,1,1, 0,4,7 and 1,0,-1

Q: Find u v, u u, ||v||, (u v)v, and u (3v). u = (3, 11), v = = (-4, 3) %3D (a) u. v (b) (c) ||v||2 (d)…

A: Given: u=3, 11, v=-4, 3

Q: The world population at the beginning of 1990 was 5.3 bilion. Assume that the population continues…

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Q: Given the series: k=0 does this series converge or diverge? O diverges converges If the series…

A: The given series is ∑k=0∞-16k. To check convergence of the series we use ratio test. Suppose we have…

Q: Verify that the two planes are parallel. --x + 6y + 2z = 7 *+ 3y + z = 8 Find the normal vector, n,,…

A: The normal vector to the plane ax+by+cz=d is given by n=a,b,c

Q: 3. Find the length of the curve r = e® for 0ses 2n.

A: Given polar curv er=eθ   ; 0≤θ≤2π

Q: Identify the inside function, u = g(x), and the outside function, y = y = (x2 – 6x + 9)2 u = g(x) y…

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Q: d d Calculate ri(t)·r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Given the function f(x) = 2x + 3 f(r + h) – f(x) Find the difference quotient f(x + h) – f(x) Find…

A: f(x)=2x+3f(x+h)-f(x)h=2(x+h)+3-(2x+3)h                     =2x+2h+3-2x-3h                      =2hh…

Q: Evaluate the integral. 9 17 1+ x2 dx V1- x2 +C

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Q: Apply Theorems 5 and 6 to find general solutions of the dif- ferential equations given in Problems…

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

Q: x- 9x + 3x? The limit of the function f(x) : as x approaches negative 3x-4+ 5x2 infinity is equal to…

A: Find your answer below

Q: Consider the following function. f(t) = 4t + 5 Find its average rate of change over the interval [1,…

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Q: Consider the following. u = (-9, -6, 4), v = (6, -7, 0) %3D (a) Find the projection of u onto v. (b)…

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Q: Determine the convergence or divergence of the sequence with the given nth term. If the sequence…

A: an=nqen limn→∞an=limn→∞nqen = 0 [when x tends to infinite ax>xa (where a is positive constant)]…

Q: The diagram at the right represents the height of a blimp flying over a football stadium. Find the…

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Q: 4x2 + 4x 7 If y = find: 6 5x dy %D da

A: Consider  y=4x2+4x-76-5x

Q: Find the area between the graph of f (x) = 10 – x² and the x-axis over the interval [-3,3]. area =…

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Q: п+1 Given that 0.47199 determine the value of ) n +1 n3 n=3 n3 n=5

A: Given: ∑n=3∞ n+1n3 =0.47199 To evaluate: ∑n=5∞ n+1n3

Q: Verify that the two planes are parallel. -x + 6y + 2z = 7 Ex + 3y +z = 8 Find the normal vector, n,,…

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Q: Use the Lagrange multipliers to find the maximum and minimum values of f(x, y) = 2x + y - 2z subject…

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Q: dx 7. S; x³ Vx2-4

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Q: 2. If f(x)=sqrt(x), which of the following is the simplified form of the difference quotient? *

A: Function f(x)=x

Q: 10. xy' + 2y = 6x²/y

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Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction I|v|| =…

A: The objective is to find the vector v.

Q: Consider the following. f(x) = 2x - 5 h(x) = x2 - 1 2x - 5 g(x) : x2 - 1 Find f'(x) and h'(x). f'(x)…

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Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). %3D v= (0, 6) %3D b =

A: Explanation of the answer is as follows

Q: Evaluate the line integral fe 3y dx + z? dy + (25 - x) dz over the quarter of the circle of radius 5…

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Q: Consider the following. u=i+j+k v = 2i +ì-k Find u x v. Determine if uxv is orthogonal to both u and…

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Q: Find the mass of the sphere x2 + y2 + z2 = a2 where the density at any point is two times the…

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Q: If 0 = then sin(8) = cos(e) %3D Give exact values. No decimals allowed! Submit Question

A: Given θ=2π3We can convert given raidans to degree. So, 2π3=2*1803=120°120=180-60We know that…

Q: Let F = sin (2x + 4z) i – 8ye** k. Calculate div(F) and curl(F). (Express numbers in exact form. Use…

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Q: The function f(x) is continuous everywhere. FALSE O TRUE 3.

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Q: Find the component form and magnitude of the vector v with the given initial and terminal points.…

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Q: Evaluate the definite integral. 7t O e7 i - elj+ 1 k 2 7 O e? - 1 i+ (e 7 1 + k 2 O e' - 1 i - 7 1 k…

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Q: fy any asymptotes, ex

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Q: 1. Find the average value of f(x) = on [0, 1].

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Q: An integral is given that can be evaluated using integration by parts. Write expressions for u, du,…

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 4 -*+ 3y + z = 5 Find the normal vector, n,,…

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Q: Determine the integral of the ff. fun 1. S- 6 dx 2. S 5 x4 dx 3. S ( 4 x7 + 7 ) dx

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Q: The other type of question in chapter 7 is solving trigonometric equation. We will not be practicing…

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Q: (-1)" Clasificar la serie como absolutamente o condicionalmente convergente E1 n5 O Diverge O…

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