Determine the convergence or divergence of the series. (If you need to use co or -00, enter INFINITY or -INFINITY, respectively.) Σ (-1) +1n n = 1 Vn lim %3D n- O converges O diverges

Q: 4x² + 21x + 54 dx x² + 6x + 13

A: The given integral is  (4x2+21x+54)/(x2+6x+13).

Q: Find a positive number z such that the sum of its reciprocal and 5,324 times its square is as small…

A: Let the number is x than we need to minimize function f(x)=1x+5324x2, x≥0

Q: In a certain bacteria culture the rate of increase in a number of bacteria proportional to the…

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Q: f(x) = 10/10x³ + 6x*

A: Follow the procedure given below.

Q: I. Evaluate the following. 3450°-j12 a. 14 + j2 – -j15 (3450°-j12) b. j2 x 32-25° -j15 5-j2…

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Q: Given the triangle below, find the angle 0. 4 Give your answer in degrees rounded to the nearest…

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Q: Find the angle 0 shown in the right triangle below. 10 Give your answer in radians and rounded to…

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Q: determine the area of the region bounded. show complete solutions.

A: We have to find the area of the region bounded.

Q: Solve: y" + 9y = 9csc3x O y = C1 cos3x + C2 sin3x – 3xcos3x + sin3xln(sin3x)

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Q: COMPUTATIONAL em No. 1 roblem: The concentration C of a certain chemical after t seconds of an…

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Q: | Consider the DE: x²y" – 4xy + 4y = 0. A) Verify that y = c1x* + c2x is a solution of the DE. B)…

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Q: Suppose you know F(11) = 71, F(3) = 16, where F'(x) = f(x). Find the following. (You may assume f(x)…

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Q: 1. lim cot x sinx X- x-nt cotx sinx

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Q: Find the integration 3x2 - 8x +13 xp. x3 + x2 -5x + 13

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Q: Use the function value to find the indicated trigonometric value in the specified quadrant. Function…

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y2 + z² (9,…

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Q: y" + 3y' + 2y = 12x* %3D y" + 4y' + 4y = e¬* cos x

A: As per the guidelines I am supposed to do the first problem in case of multiple problems. So here I…

Q: dw dw and dv du Express as functions ofu and v. dw du dw dv dw dw Evaluate and du du (Type an…

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Q: y = x² – 14x , y = 0 3D0

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Q: rapidly at Po, Then find the derivatives of the functions in these directions f(x, y) = x²y + e" sin…

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Q: Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(X), and…

A: Topic = Algebra Px=Dx·Qx +RxPx=-x2+x-3+8x+1

Q: Find the area, A, of the region enclosed by the cardioid r = 10 + 10 cos 0. NOTE: Enter the exact…

A: solution given below

Q: A model for the height h (in feet) of a Ferris wheel car is  h = 70 + 70 sin(4?t),  where t is the…

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Q: Evaluate (S (x + 2y)dy) dx. О а. 5/8 ОБ. 8/5 Ос. 3/16 O d. 16/3

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Q: Use the function f and the given real number a to find (f ) (a). (Hìnt: See Example 5. If an answer…

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Q: Find an equation of the circle whose diameter has endpoints (-1, 3) and (1, - 5).

A: The circle whose diameter has endpoints -1,3 and 1,-5

Q: | 2f(x) + ldx

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Q: Find the most general antiderivative of the following functions. (d).r(θ) = (sec θ − tan θ)^2

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Q: Sketch both parametric curves below. Then determine if they intersect. If ney intersect, find the…

A: To solve the following problem

Q: (a) Find the second derivative of the function y = 2x sin(x). (b) Find the derivative of the…

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Q: Which of the following is continuous at all points? x²-4x-5 x2+2x-35 A) f(x) = B) f(x) = x-5 x-5…

A: Note : “Since you have posted multiple questions with multiple sub-parts, we will solve first…

Q: 2. y = x+2 sin r, 0<x <T

A: To determine the area of the region bounded.

Q: consider a ctosed Kectangutar box with a Hew.y squar bare If base side ir measured with error at and…

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Q: Evaluate x dx / square coot ( x -8x )}. A. Square root of (x2 + C B. Square root of (x2- + C C.…

A: Given problem:- Evaluate ∫ xdx/square root(x2 -8x)

Q: EXERCISES 2: Find the derivative of the function at Po in the direction of A. 1. f(x, y) = 2xy –…

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Q: As the biologist for a certain crocodile farm, you know that its carrying capacity is 20,000…

A: In order to solve this problem we need to use the given formulae.

Q: b. f(x) = xe-*, g(x) =; -1<x< 5. Show in a single space. 2x

A: Given

Q: Consider the following theorem. Theorem If f is integrable on [a, b], then f(x) dx : lim f(x;)Ax n-…

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Q: 18 -19) In which of the following intervals is f(x) = continuous ? A) -3 <x < 3 B) –7 < x<7 C) 1<x<…

A: Given problems:-

Q: Mary Katherine has a bag of 3 red apples, 5 yellow apples and 4 green.apples. Mary takes a red apple…

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Q: Find a positive number a such that the sum of its reciprocal and 5,324 times its square is as small…

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Q: Find and describe the intersection of the following line and plane: T:2x+3y-4z =-7 and r = (4,2,5)…

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Q: Find the absolute maximum and minimum values of f(x) = -(x² + x) interval [-3, 4]. over the absolute…

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Q: for what value of x does the function  f(x) = 1/3 x3 - 4x attain the absolute minimum in the…

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Q: Find the gradient of the function at the given point. g(x, y) 6xey/x, (1, 0)

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Q: The graph of a function f is given. 10 Estimate f(x) dx using five subintervals with the following.…

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Q: Given the following question complete the integral and give the solution: Problem 1. Evaluate , S,…

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Q: can

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Q: 6. Which of the following vectors are linear combinations of the vectors in S? 6. a. v = | 5 T;S =…

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Q: Find the tangent lines. To the cubic y=x³-2x+3 parallel to the line 10x-y=3

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