Use either the divergence test or the integral test to determine whether the series converge or diverge. Explain why the series meets the hypotheses of the test you select. ∞ k=1 tan-¹k 1+k²

Q: Determine whether the interval [2, 2.01] is finite, countably infinite, or uncountable. Find a…

A:

Q: Determine whether the series converges. (5) k=1 3k+2 2k-1 k

A:

Q: 1 If p is an even integer and q is an odd integer, then p3 + 2q2 is an even integer.

A:

Q: Six stand-up comics, A, B, C, D, E, and F, are to perform on a single evening at a comedy club. The…

A: Prob of event = favourable conditions/ total conditions

Q: the value of a in f(x) = 3x² + ax-4 so that the average rate of change of the function on the…

A:

Q: Let L be a straight line in the Cartesian plane. Fully describe the topol- ogy that L inherits as a…

A: Let L be a straight line in the plane.  We have to find out the topology which L inherits as a…

Q: 4. How many 6-digit numbers (using 1,2,3, ... ,9) are there if repetition is not allowed? How many…

A: As in the text, two Que 4 and 6 are asked t solve. We shall answer one Que only eg 4• it has also…

Q: Match the equation with its graph. ฿ +2²=1 0 + 16

A: Ellipsoid:    An ellipsoid is a 3D geometric figure that has an elliptical shape. An ellipsoid has…

Q: 28) (a) Is the graph pictured below a function?_ 8(66) 4 1. 0 -1- -2- -3- 0 Why or why not. (b) What…

A:

Q: 2) y' = e²x-1y²

A: Solution to the differential equations by using variable separable form

Q: 1. A house has an electricity bill of 120 euros a month. 47 % of this goes into electrical heating.…

A: Percent: It is the 100th part of a quantity. It is represented as "%". To determine the percent of a…

Q: Find the absolute maximum and minimum values of f(x, y) = x³ + y² + 8 on the set D where D is the…

A:

Q: A ternary string is an ordered string of characters which consists of digits (0,1, or 2). For…

A:

Q: Make a partial depreciation schedule for the third year using the​ units-of-production depreciation…

A: Given Data: Units of production method: A   Cost    ​                          $42000 B   Residual…

Q: A sausage company makes two brands of sausages: Link and Patty. Link brand uses 1 pound of pork and…

A: Let pound of Link sausage be X1 while pound of Patty sausage be X2. Max Z =   3 x1 + 2 x2…

Q: Supply for a product is given by 2p − q = 50 and demand is given by pq = 100 + 20q. Suppose costs…

A: At equilibrium, the supply price is equal to the demand price and the supply quantity is equal to…

Q: Consider the system of linear equations [8 a 0;a 2 -1;0 -1 2/3] column[x y z] = column[1 2 3] For…

A: The given system of linear equations, 8a0a2-10-123xyz=123 We have to find the values of a for which…

Q: The demand and supply functions for your college newspaper are, q = -8,000p + 1,500 and q = 3,000p +…

A:

Q: Consider the solid generated when the region enclosed by y = √x, y = 2 and x = 0 is revolved about…

A:

Q: Verify the divergence theorem for the function A = ra, + r sin 0 cosa, over the surface of a quarter…

A: We have to verify divergence theorem for the function A=r2ar+rsinθcosϕaθ over the surface of quarter…

Q: Question: 2. Use the Newton's method and Secant method to find solutions to within 10- for the…

A:

Q: 19 1 Let ū= 0 0 3 0 v=1 0 " and w = 1 0 19.1 Describe span{u, v, w}. 19.2 Is {u, v, w} linearly…

A: In this problem using definition of linearly independent set we can find the solution.

Q: 4. Determine whether the following series converge absolutely or conditionally, or diverge. Give…

A:

Q: The power in an electrical system varies jointly with the current in the square of the resistance.…

A:

Q: a) 10 samples of different pastries are on display as customers leave a bakery, they are told that…

A:

Q: The average typing speeds S (in words per minute) of a typing student after t weeks of lessons are…

A: The graph containing the data points and the model is given by -

Q: (a) (5.18) Find the Newton's Divided Difference interpolating polynomial for the points (-h, 0), (0,…

A: (a) x                  fx                    1st order                                  2nd order…

Q: Prove or disprove the following, Vx, y, z ≤ Z(((x+y) | (y+z)) → (x | z) V (y > 0))

A: Consider        x = 3, y = -2, z = 10      Then, x + y = 3 + (-2) = 3 - 2 = 1                 y + z…

Q: Use the summation formulas to rewrite the expression without the summation notation. S(n) = n = 10 n…

A:

Q: 1. Suppose a is a positive integer. Simplify the expression a Σ((n + 2)³ +n³-2(n+1)³). n=1 [Explain…

A:

Q: 1 If n is a natural number and n ≥ 2, then (2n, n²-1, n²+1) is a Pythagorean triple.

A: The details are given in step 2.

Q: 3. (a) Find the real Fourier series of the function -2x - 4 if - 2<x<0 if 0 < x < 2 2x - 4 f(x) =…

A:

Q: This extreme value problem has a solution with both a maximum value and a minimum value. Use…

A:

Q: Use a fixed-point iteration method up to six iteration to determine a solution for x-3x²-3-0 on [1,…

A:

Q: Find the Fourier Cosine Transform of the function -mx f(x) = (ae-m +be¯¹x}³_if_x>0 if a = 5, b = 4,…

A:

Q: Find the Fourier series representation of the periodic function below. Then, evaluate the first few…

A:

Q: 6. (1 7. Find the matrix P of the orthogonal projection onto the line spanned by w = 3 Find the…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 13. Solve the initial-value problem dY dt -4 where the initial condition Yo is: (a) Yo = (1,0) (1) Y…

A:

Q: Suppose a is a positive integer. Simplify the expression a Σ((n + 2)³ + n³ - 2(n+1)³). n=1 [Explain…

A: ∑n=1a((n+2)3+n3-2(n+1)3) =∑n=1a[((n+2)3-(n+1)3)-((n+1)3-n3)]…

Q: 2. Use bisection method up to seven iterations x-2x³-4x²+4x+4=0 on the interval [-2, -1]. to find…

A:

Q: Find all the solutions of 25+2=4+42²48=²47162+32=0 in the form of xtiy

A: Z=-2 is real root then factor in irreducible form after that using quadratic roo

Q: Gaussian elimination with partial pivoting is applied to the matrix [2 1 0 3; -5 1 2 0; -2 0 1 2; -4…

A: From the given data we have to find a matrix which is obtained from given matrix by using Gaussian…

Q: For the function f(x,y) = 100 - x^2 - y^2 a) Draw the cross-section of f(x,y) with x fixed at x =…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: Determine the binary notation for 610. Enter your answer as a base-two number but do not include the…

A: We will use the concept of radix representation  of numbers to write binary notation for 6.

Q: 4) xydx − (x² + 3y²)dy = 0

A:

Q: III. Consider the function g(x) whose graph is shown below. The domain and range of g (x) are 49 R…

A:

Q: Reverse the order of integration in the following integral. Do not evaluate. 2³-3x dx dy [T

A:

Q: Solve the following differential equation: ?′′′ +2?′′ +5?′ −26?=0

A:

Q: When f(x) = ax^3− x^2 + 2x + b is divided by x – 1, the remainder is 10. When, it is divided by x –…

A:

Q: Compute the following: (a) Integrate the following vector field F = 2x cos(2)i + 2y cos(z)j — (x² +…

A: (a) Line integral along a curve C. (b)~using Gauss Divergence theorem  V is a volume bounded by a…