1. Apply the Divergence Test to the following series: 7 – 4n (2) Σ 2n + 4 n=1 (b) Σ n=1 303 +5 n2 – 15

Q: Apply the chain rule, in Leibniz notation, to determine dy dx at the indicated value of x. y = 4u(3…

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Q: (Calculate the limit lim x²+x+12

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Q: 21. Analyze the function below based on the following headings: domain, x & y intercepts, critical…

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Q: Differentiate f(x) = CH +5 -X+1 K x + 64 3 7 2x + 320x²+2x 4 3 3x pa 64

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Q: 4. (20%) Derive the quotient rule du dv V -U dx dx V² dy dx = (la) if y = 40 (1b)

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Q: 0 = * 0 Consider the angle shown above measured (in radians) counterclockwise from an initial ray…

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Q: The length ℓ, width w, and height h of a box change with time. At a certain instant the dimensions…

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Q: Determine the values of x for which the function (x) = sinx can be replaced the Taylor polynomial x³…

A: Given:function Taylor polynomial To find:values of x for which the function can be replaced by the…

Q: If f(x) = 3 + - LO 5 5 2 12 3 Find f'(3). x 5 6 + X 22 find f'(x).

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Q: · 5x³ + x² + 16x +3 dx (x² +3)² Use the following PFD form as your first step and then begin by…

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Q: Find if the series converges or diverges.

A: The answer is given below.Explanation:

Q: Determine if the series converges or diverges.

A: Refer to explanation block Explanation:

Q: f(x) =x+ 2 cos x, [0, 2π]

A: Let a function f( x ) For concave up For concave down For Inflection points

Q: Find the area of the region enclosed by the curve y = 6x - 3x² and the x-axis Sketch the curve with…

A: Given region bounded by

Q: Find the length of the curve. L = r(t) = (2 sin (t), 7t, 2 cos (t)), -4≤ t ≤ 4

A: The curve is defined by  .Find the length of it.

Q: Find the limit, if it exists, or type 'DNE' if it does not exist. J lim (x,y)→(0,-4) ev1x²+5y²

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Q: 2. Consider the sequence 2,2 + √2,2 + √√2+√√2,2+√√2+√√2+ √2,.... Assuming that the sequence…

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Q: T - Given sin x dx = 2, determine the values of the following integrals. Be prepared to give an…

A: Given integral Given graph

Q: In Exercises 7-16, convert to rectangular form. 8. 2 sin 03 cc 7. r = 2 cos 0 9. r= tan 0 10. r = 4

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Q: Use a graphing utility to graph f(x)= and slope agree with the value and slope of fat x = 8. Select…

A: The given function .The objective is to sketch the graph of the function and the first-degree…

Q: The temperature at a point  (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its…

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Q: Q/find the integral (After integration with the substitution X = 25 in U 4√2 3 2 (4- x²)³/2 dx -2

A: The given integral is

Q: Find the linearization L (x, y) of the function f (x, y): = L (x, y) = 68 - 1x² - 4y² at (4, -3).…

A: The linearization of f(x,y) at (a,b) is given byL(x,y) =f(a,b) +fx(a,b)(y-b)

Q: Could you explain how you got 2/5 from -2/5* ln(4) + 3/5*ln(4)? Whenever I add just the fractions on…

A: Given:To find:solve the expressionThe log rule-

Q: → b) f(x) = (5x-3) 5 (3x - 1)³

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Q: Test for convergence or divergence with the Direct Comparison Test.

A: The test is inconclusive based on DCT.Explanation:Taking note of the direct comparison test, for two…

Q: If f(x)= 5x sin x cos x, find f'(x) and f'(3)

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Q: y = tan 8' [0, 2]

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Q: Find the area of the segment of a sphere formed by revolving the graph of y = √49 - x², 0 ≤ x ≤ 6,…

A: To find the area of the segment of a sphere formed by revolving the graph of ​, , about the…

Q: Find the Maclaurin polynomial of degree two for the function /(x) = sec (9x). Select one: O a. O b.…

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Q: What curve do the parametric equations trace out? Find the equation for the curve. x = y = 12 + cos…

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Q: (x) X

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Q: 1 Given the geometric sequence: 10, ¹40 Find an explicit formula for an, where the first term is a₁…

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Q: Express the integrand as a sum of partial fractions and evaluate the integral. √²+2y+81 (y² +81)² dy…

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Q: Start with a line of length 19. Fold it twice to make an open topped rectangle. What is the max…

A: The objective of the question is to find the maximum height, length, and area of an open-topped…

Q: For the curve given by r(t) = (5 sin(t), -3t, -5 cos(t)), Find the unit tangent T(t) = (000) Find…

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Q: α. Σ=of (2k) b.Σ=2f()_c.Σ=19(f(k)).

A: we need to evaluate the sum."Note that as per the rules, we are supposed to answer the first three…

Q: Find a positive value of k such that the average value of f(x) = √6x over the interval [0, k] is 20.…

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Q: A Ferris wheel has a radius of 31.2 feet. The bottom of the Ferris wheel sits 0.8 feet above the…

A: We need to solve Ferris wheel problem.

Q: Determine the equation of the tangent to the curve y= (2x^2-3)(x+1)^2 at the point where x=1 Thank…

A: The equation of the tangent line to a function y= f(x) at (a,b) is given byy - b = f'(a)(x - a)

Q: Solve cos(8) decimal places. 0 0.2 for solutions on the interval 0 ≤ 0 < 2. Write your answer(s) in…

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Q: The following table shows the results of a survey of authors by a (fictitious) publishing company.…

A: The objective of the question is to find out the percentage of established authors who are…

Q: 21. Find a and b such that [-1, a, 6] and [b, 8,12] are collinear. 22. Determine the area of AABC…

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Q: A country's production of solar power, in megawatts, can be modeled by f(t) = 350(1.3)', where t is…

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Q: Use the definition to find the Taylor series (centered at c) for the function. f(x) = ex c = 0

A: The given function isThe centered value is

Q: The position function of an object is given by 5(1) - (2² − 1 ) ( ¦ + 3). distance, s, is in metres.…

A: The position function of an object is given by , where time, t, is in seconds and distance, s, is in…

Q: Find if the series converges or diverges.

A: Answer: the series divergesExplanation:Method 1: Method 2:  Note: there is is various way to prove…

Q: Suppose ƒ(x, t) = xª sin(5t). (a) At any point (x, t), the differential is df = (b) At the point…

A: The given function is .

Q: Q1. Find the general solution of the following differential equations and then find the particular…

A: Note:-Since you asked multiple questions which are not interlinked, according to our policy we can…

Q: 3) What does the matrix 1 0 0 0 1 0 001 represent?

A: The matrix represents the identity matrix of size 3x3.Explanation:In the given, the matrix…