Find the limit. NOTE: Enter the answer using round brackets. t2 + 3 1 lim t→+∞\ 7t2 +8'8t (?, ?)

Q: Find the general solution of d²y dy 4- + 4y = 0 - %3D dx?

A: The given differential equation is d2ydx2-4dydx+4y=0.

Q: Sketch the region R of integration and switch the order of integration. f(x, y) dy dx y Show ,…

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Q: ques

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

A: Here, note that the sequence an is convergent if  limn→∞an ia finite,

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Q: Given h(x)dx=- and G(x)dx =What is [8h(x)-3G(x) ]dr? 3. %3D O Cannnot be determined O 2 O none of…

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Q: Suppose that the monthly cost, in dollars, of producing x chairs is C(x) = 0.002x + 0.07x + 19x +…

A: We have to solve only D, as asking in the question.

Q: Write the equation of a sine or cosine function to describe the graph. `y 10n 3 3 3 \3 -1 -2

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Q: Find the vector component of v = (4, – 1, 7) along b = (6, 6, –7) and the vector component of v…

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Q: f(x)=(x^2+10x+1)e^-x Find the critical points and determine whether it is a local maximum, local…

A: Critical points are points where the function is defined and its derivative is zero or…

Q: 8. Find the dimensions of the rectangular box, open at the top, which has a maximum volume if…

A: Given surface area is 18 square feet.

Q: John and Lashonda are standing on a riverbank, 130 meters apart, at points A and B respectively.…

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Q: Find all points the graph of f(x) = 2 sin x + sin?x where the tangent line is horizontal on

A: Solved below

Q: Consider a triangle ABC like the one below. Suppose that a=32, b=31, and c= 18. (The figure is not…

A: The given question can be solved as shown in step2.

Q: 2. There is an element from the group Qu of order: (a)3 (b) 5 (c) 6 (d) 4 The correct answer is (a)…

A: We know order of an element in a divides the order of the group. We know center of Sn is trivial for…

Q: Given: 6n An = 12n + 13 For both of the following answer blanks, decide whether the given sequence…

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Q: 10 | f(x)dæ 43 what is 11' Given that f(8)ds? 10 answer -

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Q: Evaluate the integral. 3 (x³ - 6x)dx

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Q: Find the indicated derivative for the function. f′′(x) for f(x)=2x7−9x2+2x−

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Q: Let f be integrable on [-a,a]. If f is an even function, then f(x)dx is equal to a -a 2 f(x)dx

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

A: This is a problem related to cross and dot product of the derivative function. Please find the…

Q: 2. What is the extraneous root of 2 log3(x + 4) - log3(-x) = 2?

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Q: Find the directional derivative of f at P in the direction of a. f (x, y, z) = xy + z?; P(2,5, 2); a…

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Q: (A) Find the dimensions of a rectangular box with square ends that satisfies the delivery service's…

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

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Q: Find the absolute maximum and absolute minimum values of the function, if they exist, over the…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. an = 8^(n +…

A: The given sequence,    an=8(n+2)9n

Q: Find the Taylor series centered at x 3 for the given function. f (x) = In(x+ 2)

A: Here, the given function is: f(x)=ln(x+2) Now, f(3)=ln(3+2)=ln…

Q: First four terms of the sequence n2+3 n 1+8 n are: 4 10 79 28 9 17 75 33 none 4 10 18 28 9. 17 25 33…

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Q: Suppose F is an antiderivative of f(x) = VT. If F(0) 1 then F(1) 4 %3D %3D is 3 A. –1, B. -, C. 0,…

A: Let f be a function . Suppose F is a function such that  F'(x) =f(x) then F is an antiderivative of…

Q: if S f(X) dx = 36 and 9(x) dx=13 find So [4f(x) +69(x)] dx %3D

A: ∫064f(x)+6g(x)dx=4∫06f(x)dx+6∫06g(x)dxSubstitute ∫06f(x)dx=36 and ∫06g(x)dx=13

Q: 3. Find the equation of the tangent plane and the equations of the normal line to the surface z = In…

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Q: A region bounded by f(x) = 3 - x, y = 0, and x = 1 is shown. What is the volume of the solid formed…

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Q: Use the comparison test to verify that the following series converges: 1 Σ n=1 5+n4

A: We have to check the convergence

Q: 1) Verify that the function f(r) = r - 3x + 2 satisfies the hypotheses of the Mean Value Theorem on…

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Q: Preview Activity 1.3.1. Suppose that f is the function given by the graph below and hat a and a + h…

A: Given, y=f(x) is the function with the graph. a and a+h are the input values(x-values).

Q: Use the formula k(t) = ||r' (t) × r"(t)|| to find k(t). 13 ||r(t)||* r(t) = t'i + t6j K(t) =

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Q: 1 0.5 -5 -3 1 2 f -0.사 -1 -1.5 Find the following limits, if they exist. 7. lim f(x) 8. lim f(x) I-1

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Q: 11 of the distance from which it 12 A Super Happy Fun Ball is dropped from a height of 5 feet and…

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

Q: 10. On a typographic map, the contour lines show changes in elevation of the land. You and a friend…

A: a) From the figure I have an elevation of 200 ft and the elevation of my friend is = 800 ft. So the…

Q: Let vector Ñ be normal to plane x – 5y – 2z = 3, and let Ē = (3, – 2, 1). Find the following. 1. The…

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Q: Using a model of the prototype ball thrower, a ball is fired into the air with an initial upward…

A: Given that height of the ballht=-16t2+48t+41.if balls reaches maximum height then…

Q: The 3rd term of an arithmetic series is 34 and the 17th term is -8. Find the sum of the first 20…

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

Q: divergence. , (-1)"-1 R 2n Test the series for convergence or

A: Here we use the ratio test for convergenceFor a series ∑an  then limn→∞an+1an=L then (i)  if L<1…

Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. y y = fx) 8.…

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Q: y a+h Figure 1.3.2: Plot of y = f(x) for Preview Activity 1.3.1. b. Construct a right triangle whose…

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Q: a, = V 2n + 6" %3D lim an %3D

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Q: 2. Suppose that you are told the matrix a b с-26 A = с 2b — а -a – 2b + 2c b a+2b 36 has an…

A: The given matrix,   A=abc-2b3bc2b-a-a-2b+2cba+2b