Given the power series Σ 4" (x)" n =0 n! Find the "Interval of Convergence" for the series.

Q: If the average value of a function f(x) is 3 on the interval [0,1] then the average value of f(x) on…

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Q: Consider the following planes. -2x + y + z = 2 10x – 5y + 2z = 4 (a) Find the angle between the two…

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Q: 1 31 41 В' 25' 32

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Q: Below is the graph of the derivative f'(x) of a function defined on the interval (0,8). You can…

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Q: 9. Which phrase best describes a function which has the following table when it's graphed. |-2 -1 -1…

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Q: Find the exact length of the curve. x = 8 + 12t2 y = 3 + 8t3 Osts 3

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Q: Hw) Salvethe diffequ

A: We need to solve D.E.

Q: 2. Is the function f(x) =² continuous on the closed interval [-1, 1] ? Draw its graph illustrating…

A: Given problem:- Is the function ƒ(x) = 3/x continuous on the closed interval[−1, 1]? Draw its graph…

Q: Determine whether the series 2 (n + 1)/n converges or diverges. n= 1

A: Explanation of the answer is as follows

Q: Find the derivative of y= e^x * sin(x) y= 5x^2 + cos(x) y= sec(x) + csc(x) y=…

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Q: < CO R # 3 At what points of R is the following function continuous? f(x,y) = /6x2 + 3y² %3D Select…

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Q: Find the marginal revenue for producing x units. (The revenue is measured in dollars.) R = 30  10x −…

A: Given that, R = 30(10x − x3⁄2)

Q: Use the Laplace transform to solve the initial value problem y''+y'−2y=2e3t,y(0)=−1,y'(0)=4 y(t)=

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Q: A company introduces a new product for which the number of units sold S is given by the equation…

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Q: MY NUTES A projectile is shot upward from the surface of Earth with an initial velocity of 110…

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Q: Which one is the sum of the geometric series 1 00 n= O 2 O 3 | 2 O Divergent 3/4

A: The sum of an infinite geometric series is given by, Sn=∑n=0∞arn=a1-r if r&lt;1 a is the first term…

Q: Let P denote the plane in R3 containing the points (1, 2, 0), (3, 4, 1), and (−1, −2, 1). (a)  Find…

A: Given that P denote the plane in R3 containing the points (1,2,0) , (3,4,1) and (-1,-2,1) .

Q: Use the General Power Rule to find the derivative of the function. y = 12 3 4x2 + 7 y' =

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Q: Find the gradient of the function at the given point. w = x tan(y + z),    (17, 3, −1) ∇w(17, 3,…

A: Given  w = x tan(y + z) We have to find the gradient of the function ∇w(17, 3, −1).

Q: The series 5 n 6. n=4 8

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Q: Determine the convergence or divergence of the series. (If you need to use o or -00, enter INFINITY…

A: Given: Now,             limn→∞ 8n-13n+1=limn→∞ 8-1n3+1n=limn→∞ 8-1nlimn→∞ 3+1n=83 So, the series is…

Q: A college student borrowed $44,000 to pay for tuition, room, and board. Some of the money was…

A: A college student borrowed $44,000 to pay for tuition, room , and board. Some of the money was…

Q: Let g(x) 8 In(t) dt. Use the Fundamental Theorem of Calculus tc g'(x) =

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Q: 1. (a) Find a power series representation for f(x) %3D 1+ x3 (b) By differentiating the power series…

A: Let's find.

Q: 10 emann sum of the integral using the given value of n. J, x+2

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Q: Test the series below for convergence using the Ratio Test. n+ 2 34n +3 n=1 The limit of the ratio…

A: To determine the series converges.

Q: Find the derivative of the function. y = 4t   t + 7 y' =

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Q: i) The area of the surface obtained by the rotating the curve y=V 16-x², -1s×<1 about the x-axis is

A: As per the company's guidelines, we are supposed to solve first question for you,  kindly repost the…

Q: A particle moves in a straight line with velocity t-2 – * ft/s. Find the total displacement and…

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Q: Find the critical point of the function f(x,y) = 3x2y2 + 2y2 + 2x2. a. (0.82,0) b. (0,0) c.…

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Q: 5. A farmer wishes to fence off a rectangular region next to a straight wall. The side of the…

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Q: 33 1 2s5 6s3

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Q: 1. Solve for y3 using the method of successive approximation. dy = x + y; y(1) = 1 dx ANS: y3 = 1+…

A: We have to find y3.

Q: Find the indicated terms of the geometric sequence with the given description. The third term is…

A: To find the indicated terms of the geometric sequence with the given description. The third term is…

Q: 4. Suppose the function is defined by y = f(x) = x² – x a. Find the average rate of change of y with…

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Q: Test the series below for convergence using the Ratio Test. S In(n) 6h n=2 The limit of the ratio…

A: Given: Now,             limn→∞ lnn+16n+1lnn6n=limn→∞ lnn+16n· 6lnn6n=16·limn→∞…

Q: 4. A sawtooth wave is a kind of waveform that ramps upward and then drops off sharply. They are…

A: According to graph we see that  simpson's 1/3 rule is best method for accurate result .

Q: The tangent line to the graph of y g(x) at the point (4, 2) passes through the point (1, 4). Find…

A: Tangent line to graph g(x) at a point (4,2)⇒(4,2) is point on g(x)g(4)=2

Q: Which one is the arc-length of the curve y =2/7x + 11, x E [7, 11]? 147x+280 dx 7x+ 11 14x2 +…

A: The curve y=27x+11 , x∈7,11

Q: (2x- 1)dx, n = 4 Calculate the Riemann sum of the integral using the given value of n.

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Q: 3. S(3Vx + dx 2 (x+3) + C

A: Topic = Integration As per guidelines , At a time only one question can be answered out of different…

Q: Graph the region bounded by r= 6cos3θ

A: We have to graph the region bounded by  r = 6 cos 3θ.

Q: Find the limit of the sequence if it converges; otherwise indicate divergence. an = (-1)" (- %3D

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Q: y = 4e" Vx et y = x2 – 1 x2 – 1

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Q: dx 6. S e2x+1

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Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x – 1) + 2* – x has a critical number…

A: Find your answer below

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

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Q: Determine whether the (-1) "3" 00 geometric series * is convergent or n=1 6" divergent, and if it is…

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Q: -2n f) S“ cos 2x dx g) S et² t dt h) S x sin(x²) dx

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Q: 5 s2+ 3 s2 –8

A: Let's find.