1. If lim ana then lim an+10= lim an-10 = a. n4x 84x 818 2. Let A CR. If a is a lower bound of A, then it follows that -a is an upper bound for A. 3. Let S be a nonempty bounded subset of R. If for every e > 0, there exists an x ES such that x>b-e, then b = sup S.

Q: A vertical right-circular cylindrical tank measures 32 ft high and 10 ft in diameter. It is full of…

A: I have explained everything with in the solution .please go through that.

Q: Solve the heat flow problem shown below with ß= 3, L=x, and the given function f(x)=2 sin (x) - sin…

A:

Q: 1. In Mathville, the time for the sunrise for any day during the year can be modeled by the formula;…

A: The given function is t=1.26sin2π365d-81+7.2. (a) To Find: Earliest and latest sunrise time during…

Q: In the process of proving P(n) by induction, we need to assume that P(n) is true and show that…

A:

Q: 14. y"+y = sin t y(0)=2_y'(0) = -1

A:

Q: solve the following equation In(t) = 3

A: The given equation is ln (t)=3

Q: Find the circulation and the flux of the field F=-yi-xj around and across the following curves. a.…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Problem 1. Given z = f(x, y), x= x(u, v), y = y(u, v), with x(7, 7) = 5 and y(7, 7) = 5, calculate…

A:

Q: What is the characteristic of the ring Z4 × 4Z

A: The characteristic of the ring R is the least positive integer n such that,             na = 0 ∀ a€R…

Q: You are to roll a fair 6 sided die 50 times and record what you roll each time. You are then to…

A: Let's start with rolling a fair 6- sided die 50 times and calculating the mean of the rolls. We will…

Q: f(x, y) = (x² − 49)² – (y² – 9)² - A) f(0, 3) = 2401, local maximum; f(0, -3) = 2401, local maximum;…

A: The given function fx, y=x2-492-y2-92. To find the local minimum, local maximum, and saddle point.

Q: 6. Let A = {nk Z, n = 6k+5} and B = {nn is odd}. Prove that AC B.

A:

Q: (5) Let V=R2. For (1, 1), (2, 32) EV and c ER, define addition and scalar multiplication operations…

A:

Q: Find the scalar equation of the plane r = [-2,2,7] + s[3,-2,1] + t[-2,1,5]

A:

Q: Given that find the Laplace transform of √√cos (5√t). c{√= cos(5√²)}-0 cos(5√t) πt = e-6.25/s

A:

Q: Use the method of Laplace transforms to find a general solution to the differential equation below…

A:

Q: . Find the Laurent series of 1 ez 1' in z up to z6 and show the series converges in 0 < |z| < √√2π.…

A:

Q: Apply Simpson's Rule to the following integral. It is easiest to obtain the Simpson's Rule…

A:

Q: 1. Let I(u) = F(u'(x), u(x), x) dx. Find the first variation and Euler-Lagrange equations for each…

A:

Q: 2. Find the general solution of the given system. Use a computer system or graphing calculator to…

A:

Q: Solve the initial value problem below. 2y (3) + 4y'' = 0, y(0) = -1, y'(0) = 0, y''(0) = 1 y(x) =

A:

Q: 49. Show that the function f(x) = y=x² + 3 is continuous for x # 1, 2. Then compute the right- and…

A:

Q: Find the smallest number n of terms needed to obtain an approximation of the series accurate to 10…

A:

Q: a) Write the quadratic form 9r2+72+11x3-8x1x2+6x273 as XTAX, where X = and A is a symmetric matrix.…

A: (e) From the given Equation of conic:

Q: Solve the initial value problem below using the method of Laplace transforms. y'' - 2y' + 2y =…

A:

Q: Solve the initial value problem below using the method of Laplace transforms w''+w=3t² +6, w(0) = 3,…

A:

Q: Determine the partial fraction expansion for the rational function below. 4s + 24 (s+2) (s²+4)

A: This topic is about partial fraction of rational function

Q: Use Gram-Schmidt to find q₁, 92, 93 (orthonormal). Then write A as QR: 1 2 --83- A 0 0 5 0 11 - QR

A:

Q: The New College is letting students choose a new NewnetID username. Under the new system, each…

A: (a) In the NNewnetID usernames, the first and the last three characters are digits. So, for each…

Q: Evaluate by the residue theorem: So sin 22 da 1+2²

A:

Q: A certain college graduate borrows 7752 dollars to buy a car. The lender charges interest at an…

A:

Q: Let p be an odd prime and a, b E Z such that (a, p) 1 and (b, p) = 1. Prove that if neither x² = a…

A:

Q: (2) Find an orthonormal basis for the positive definite matrix 12 25 9 and find a coframe E that…

A:

Q: 4. If {f} is a sequence of measurable functions, prove that the set of points at which {n} converges…

A:

Q: The Laplcae transform of f(t) is given 38²-1 F(s) = s²+8+1

A:

Q: If A is a 1 x 2 matrix and the sum A + B can be computed, what is the dimension of B? X

A:

Q: • [[ √ ₂ ₁² dv Evaluate x² + y² = e² dV where E is enclosed by the paraboloid z = 4+x² + y², the…

A:

Q: -ind three linearly independent solutions of the given third-order differential equation and vrite a…

A: Given a third order differential equation is z'''+4z''-16z'-64z=0   we need to find 3 linearly…

Q: 9-23 Four automobiles have entered Bubba’s Repair Shop for various types of work, ranging from a…

A: Job 1 Job 2 Job 3 Job 4 Billy 400 90 60 120 Taylor 650 120 90 180 Mark 480 120 80 180 John…

Q: Find the growth or decay rate of the given exponential model in percent. f(x) = 0.32 (1.24)X A 24%…

A:

Q: Solve the third-order initial value problem below using the method of Laplace transforms. y'"' +…

A:

Q: Can you please solve this for C. Please do it on paper.

A: From the given information:

Q: Find 1²² x²dA where R = {(x, y) | 25x² + 16y² ≤ 400} <

A:

Q: Let P(s) and Q(s) be polynomials with the degree of P(s) less than the degree of Q(s). Let Q(s) =…

A: Given that P(s) and Q(s) are polynomials with degree of P(s) strictly less than the degree if Q(s).…

Q: Test the series below for convergence using the Ratio Test. n+5 23n+4 The limit of the ratio test…

A: I have explained everything with in the solution. Please go through that.

Q: In Z₁2, solve x² − x = 6. -

A:

Q: 1. Let I(u) = F(u'(x), u(x), x) dx. Find the first variation and Euler-Lagrange equations for each…

A:

Q: 30 + 23s + ܐܨ7 (s − 2)(s² + 25 + 5) –

A:

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" +…

A:

Q: 13. y" + 3y' +2y=6_y(0)=1 _y'(0) = 2

A: y''+3y'+2y=6y0=1y'0=2