Let p (> 0) be the first of the n arithmetic means betw numbers and q (>0) the first of n harmonic means betw same numbers. Then prove that 2 9 € [p₁ [ " + 1² P₂ р and p n- 2 9, 9

Q: 4. Derive the following formula: ° cos(ar) = cos(br) dx = (b − a) (a≥0, b≥0). - COS x²

A: Use Integration by parts to solve.

Q: Find the shortest distmee between the times 8+ = 24² 2-3 3 and २ = x-2 = y-4 4 - ५-5 and also obtain…

A:

Q: Find the area of the curved surface z=x+y^2 on a triangle with three points (0,0), (1,1), and (0,1)…

A: The given problem is to find the area of the curved surface z=x+y2 on a triangle with three points…

Q: Consider group G and its subgroup H (H ≤ G): [G : H] = 2. Prove why H is a normal subgroup of G.

A:

Q: 2. Determine the general value of the following. tan(2 - 5j)

A: According to the guideline, only one question can be answered. Please repost other question…

Q: What is the chromatic number of each graph? P5 C6 Cg K8,15 K13

A:

Q: y' – 5y” + Зу' у - (d) x²y" — Зху' – 5:

A:

Q: Select all the convergent series a. Στη 1 b. n=1 C. ΣΤΑ 1 3" n! (-1)" n2

A:

Q: - 27. Determine k so that lim (3e-kt — k) = 8118 I T 5

A: We have to find the value of k for which given limit is true.

Q: Approximate the area under the curve graphed below from x = 3 to x = 8 using a Left Endpoint…

A:

Q: Consider the following initial value problem. (A computer algebra system is recommended. If a…

A: Given Data: Let us consider the given data,  Initial Value Problem  y'=y2+2ty3+t2 , y1=2 To Find :…

Q: Use the series solution method to solve the Volterra integral equations: 호 - - f (x - 1)u(t)dt *12.…

A:

Q: APR of 4.8% compounded You are saving to buy a car, and you deposit $210 at the end of each month…

A:

Q: 3. Supply the missing integrand and limits of integration. 5 (a) [ [² 62²y dady = 2 /2 (b) [₁" ["²…

A: Here the double integration is given. If the double integration is separable then saperately…

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

A:

Q: Suppose someone takes out a home improvement loan for $30,000. The annual interest on the loan is 6%…

A:

Q: The table below shows the calories, fat, and carbohydrates per ounce for three brands of cereal, and…

A:

Q: Be V a vector space over IR, {e, S < V, dim S < dim V (m < n). em} and show Σ(ve)e, =Σ(ve)e wer j=1…

A:

Q: 4. Evaluate the iterated integral: CIE dyda.

A:

Q: The standard normal probability function is used to describe many different populations. Its graph…

A: Given that fx=13πe-x2/4.

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

A: Given That : F=4x+exsinyi^+5x+excosyj^ C: Right-hand loop of the lemniscate r2=cos2θ  To Find :…

Q: 7. ytt = 100yxx, 0 0; y(0,t) = y(1,t) = 0, y(x,0) = 0, yt (x,0) = x

A:

Q: 2 2 Find the least-squares solution of the system -6 k= 25 3 5 H -4 33 نا برا

A:

Q: 24. Write parametric equations for the line passing through the point at (-2, 5) and parallel to the…

A: The given equation is  3x - 6y =-8 which can be written as        6y = 3x +8 or, y = 12x + 43 The…

Q: Solve the linear programming problem. Maximize P= 15x+85y Subject to x5y s 10 xyzo What is the…

A:

Q: y"+2"-z' = 0 y' + z 221-ex - Yo = 0, y = 1 20= 1, 2 = 1

A:

Q: 5. Suppose that f: R→ R is continuous. and f(x) > 0.. Prove that there is an in- terval I =…

A: Used the definition of continuity.

Q: Determine whether u and v are orthogonal, parallel or neither. 33 u = (2, 18) and V =

A:

Q: Find the missing quantities by first computing the markup on one base and then computing the markup…

A: Let’s assume the selling price is ‘a’   Then Markup = a X 44% = 0.44a   Selling Price = Cost +…

Q: 5. SET-UP the double integral that solves for the volume of the solid: X 3 Z 3x+2y+ 4z = 12

A:

Q: 3. Find Taylor's series for f(x) centered at the given point a, as well as the associated radius of…

A: a fx=2cos2x, a=π2bfx=e-3x, a=1

Q: 74 72 70 68 66 Height (in inches) 2 62 60 Height = 51.46 + 1.728 (Shoe Size) ● 4 5 6 7 ▼ 8 9 Shoe…

A:

Q: Domain:[-3,0) U (0, 1) U {3U (, ∞0) Range: [-6, -3) U (-3,-2) U{-1U (1, ∞)

A: simplify what it means after the third U in both answers . like write it in another way...

Q: sequence of numbers A,, n = 1, 2, 3, ... is defined as 2n - 3 2n 2 and for each n ≥ 2, An: = en…

A:

Q: Obtain in factored form of a linear differential equation with real, constant coefficients that is…

A:

Q: A division of Ditton Industries manufactures a deluxe toaster oven. Management has determined that…

A:

Q: 4. Find MacLaurin's series (i) using the known function series (see slide 30 from the Lecture Notes…

A:

Q: Prove that: ™ [_xª−¹+ ₂F₁(a,b;c;x)]=(a)_ xª−¹ ₂F ₁(a+m,b;c;x) a-1+ dx"

A:

Q: Determine the dimensions of the least expen- sive cylindrical can that will hold 100 cubic inches if…

A:

Q: Suppose the vector field v(x, y, z) = (2x − 1) i + (−x − 3) j + (2z − 1) k represents the velocity…

A: We will use stokes theorem  f a simple, closed, smooth boundary curve C  with positive orientation…

Q: Show that the given equation is not exact but becomes exact when multiplied by the given integrating…

A:

Q: y = A sin sin 5x + Bcos 5x; + + 25y = 0

A: Since all are different so as per our guideline, we are supposed to solve only first question.…

Q: Let f(n) = 4n³ +2n² - n and g(n) = n³. Which of the following C, no prove that f(n) = O(g(n))?…

A: Given Data: Let us consider the given data, fn=4n3+2n2-ngn=n3 Prove that: fn=Ogn

Q: Use mathematical induction to prove that for each natural number n, 3 di- vides n³ +23n. Compare…

A:

Q: Find the missing quantities by first computing the markup on one base and then computing the markup…

A: As per the policy of bartleby the provisions is to solve only one question at a time now I am…

Q: 3. A spring with a mass of 2 kg has damping constant 14, and a force of 6 N is required to keep the…

A:

Q: 2. a) Give an example of a function f: R →R that is differentiable everywhere and 1- to-1, but f'(x)…

A: Let, f(x) = x3 .      Then, f(x), being a polynomial, is differentiable for all x ∈ R, i.e.,…

Q: Find all critical numbers of the function y = minimum. x²-9 -, x#5. Then use the second-derivative…

A: Solution :-

Q: Domain :[-3,0) U (0, 1) U {3U (, ∞0) Range: [−6, −3) U (−3,−2) U {-1U (1, ∞)

A: The interval notation given by a,b can be written in set-builder form as x|a&lt;x&lt;b. The interval…