6) Let A be a bounded set of real numbers. Show that both l.u.b. A and g.l.b. A are in cl A. However, show that each of these need not necessarily be an accumulation point of A.

Q: Maximize subject to: Z = $140×₁ + $150x₂ 8x1 + 2x₂ 40 9x2 + 3x₂ ≤ 120 X1, X₂ ≥0

A:

Q: 9. Diagonalize A = 11 9 3 6 14 3 -36-54-13

A:

Q: Q2: find the Laplace of the following functions: (cosw, for 0<t< a- f(x) = TC 2π 0 ,for, < t < ² W

A:

Q: What are the fourth roots of -3+3√/3i? Enter your answer by filling in the boxes. Enter the roots in…

A:

Q: 4x - 10 Let f(x) = 1-(2x-5)** a. Find the Taylor series representation for f about x = 2.5 that is…

A:

Q: USING  ALTERNATING SERIES TEST PROVE THAT THIS CONVERGES

A:

Q: Determine the Fourier Series of the function below: * X, 0 < x < T | f(x) = { π < x < 2π, = π, and…

A:

Q: Show that the substitution x=e, y=e converts the equation ди ди Hu д 2 02, +y2 +x ду2 дг +y 0 ду…

A:

Q: om the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a…

A: Given that an altitude is drawn from the vertex of an isosceles triangle, forming a right angle and…

Q: Find a closed form for the generating function of the sequence An = n3" (n ≥ 0). Clearly show all…

A: Definition: The generating function of the sequence an is, Gz=∑n=0∞anzn

Q: 2. Determine the values of ʼn and h required to approximate fx²sin (-x) dx to within 10% using the…

A:

Q: 1. Use the power series 1 (-1)-1-1, x + 1 n=1 to find a power series, centered at 0, of the…

A: We have to find the power series of given function.

Q: -=f"(() is The degree of precision of a quadrature formula whose error term is :-

A: To find- The degree of precision of a quadrature formula whose error term is: -h336f''ξ is

Q: 6) Consider the plane P: z+y-z = 0 in R³ that contains both the points P₁(1, 0, 1) and P₂(0, 1, 1).…

A: Given the plane P : x+y-z=0 and the points P11,0,1, P20,1,1

Q: 4. A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

A:

Q: Find all the local extremas and saddle points: f(x, y) = y sin x

A:

Q: 2. L{sin² = nt} 7² a. S³+π²s π² b. 772 2s3-2π²s π² C. 772 2s3+2π²s π² d. S³-π²S

A:

Q: L{12te-³t} 12 a. (s+3) 12 b. (s+3)² 1 C. (s+3)² 12 d. (s+3)³

A:

Q: or convergence of Fourier Series representation?

A: a) 1. The function should be integrate over the given interval. 2. The number of maxima and minima…

Q: Determine convergence/ divergence. If result is convergence, find the li

A: 1) The given series is: ∑n=1∞416n2-8n-3 Consider the denominator of summand 16n2-8n-3. Factor the…

Q: Determine the Fourier Series of the function below: * f(x)=, over the interval 0 < x < 27 and has…

A:

Q: Solve for the missing lengths and angles.

A: Introduction: If two triangle sides are congruent, the angles opposite these sides are also…

Q: Suppose T: RR' is a linear transformation 1 1 21 10 3 2 a) Find Null Space Nul(T) b) Find Col Space…

A:

Q: Ne the following initial value problem with Laplace transform "y" + 3y² + 2y = et, y(o) = ét;…

A: We need to solve the given differential equation using Laplace Transformation.…

Q: The function y a = -3 = ax¹ + 1 has a minimum at the point (√(√)). . Determine the value of a.

A: option(5) is correct.

Q: 11) If f is a potential function for the vector field F = (-2y + 2xyz, -2x + x²z, x² y + 8z), then…

A: To find- If f is a potential function for the vector field F = -2y + 2xyz, -2x + x2z, x2y + 8z, then…

Q: Consider the system of equations x+2y+32 = 0 2−g=0 x + kz = 0. a) Calculate the determinant of the…

A:

Q: 3. Find f'(x) and f"(x) if f(x) = ln x+2 cos³ z.

A:

Q: 5. A stone dropped into a still pond sends out a circular ripple whose radius increases at a…

A: Ans: 180πm²sec Explanation: Area of circle = πr².......  A=πr²  ----------[1] Differentiating ....…

Q: (a) Give the partial derivatives of P. Pr,s)= 2rs +². - 5s + 2 Ps(r,s)= 2² +r2s - 5r (b) Which graph…

A: To find value of s which minimize the function f(s).

Q: Optimize the function. Use cramer’s rule for the first order condition (optimal values for x1, x2,…

A: Given, y=3x12-5x1-x1x2+6x22-4x2+2x2x3+4x32+2x3-3x1x3 For optimal values of x1, x2, x3 , First order…

Q: Matching: Write the letter of the view in the box Figure #1 Figure #2 Figure #3 Figure #4 Figure #5

A: In this question, the top view, front value, and side view are to be determined.

Q: sin(2x³) x² 11. Approximate justify your result. within 0.0001 if x = 1/3 using its Mac expansion…

A: Solution: Given function is, f(x)=sin2x3x2 sin(x)=∑n=0∞-1nx2n+12n+1! f(x)=∑n=0∞-1n2x32n+12n+1! x2…

Q: 2. Consider the Transformati graph g in gr Identify all th Express g in c) How can you a) b)

A: q-2 consider the graphh of y=fx (a) identify all the transformation. original function y=fx step-1…

Q: Why is (subtracting two positive numbers that are each less than 1), less than or equal to (1 minus…

A: Since r and s are both between 0 and 1  Then 1-r is positive and also 1+s is positive  Now , take…

Q: Newton's Law of Cooling states that a hot object cools down at a rate proportional to the…

A: Solution : Given, T(t)=20+70e-0.034t a) Checking for initial condition t=0, T(0)=20+70=90 °C Which…

Q: 1. (a) (i) Determine the least degree of the polynomial function given by the following graph. (ii)…

A: The x-intercept of the graph is the point where the graph cuts the x-axis and the y-intercept of the…

Q: Properties of the Dot Product @ प.U - 044पॅ= Oor] [[-]oory ID

A:

Q: 5- dy/dt = y²(y+1)(y-3), -∞<Yo<∞

A:

Q: 3. Rhadika earns $600 per week and lives alone in a 1-bedroom apartment. Her monthly rent is $550.…

A: Solution:- Given that, Rhadika earns $ 600 per week and we consider a 4- pay month. Therefore, total…

Q: 3s+4 -s²+4s+5· a. e2t (3 cost - 2 sint) b.e-2t (3 sint 2 cost) c. e2t (3 sint - 2 cost) d.e-2t (3…

A:

Q: Q/ Provethet f is continuous if f(B) = f'(B) Suppose of continuous and Prove F(B) ≤ f(B) then for…

A:

Q: 1. Answer the following: (a) If you are given a differentiable function f, give at least one…

A:

Q: 3: Using Laplace Transforms, find the solution of the initial value problem: d²y dx² +9y 9. sin(t).…

A:

Q: 7. Is it possible for a graph with six vertices to have a Hamilton Circuit, but NOT an Euler…

A:

Q: Direction: Determine whether the given statement is a tautology, contradiction, or contingency.…

A:

Q: 5-1. y" - 4y + 4y = t³e²t, y(0) = 0, y'(0) = 0

A: Since  you have posted a multiple  question according to guildlines I will solve first   question…

Q: 22. Convert 0.6667 to a fraction. 23. Convert 0.75 to a fraction. 24. Convert 5.3333 to a mixed…

A:

Q: 1. Consider finding the root of f(x)=x²-3. Let Estep=0.01, Eabs = 0.01 and start with the interval…

A: Given,        f(x)=x3-3  and with the interval 1, 2.

Q: 3. Find f'(x) if f(x)= 2x + sin³ a

A: This question related to derivation.