8l A formur wants to buildariding arena n the Shape of a rectapgke toppecl by two simicirelese find the maximum possibluareaof Such an enclosune if 'the farmme r has b00 ft of fenany Avalble

Q: (Rudin, Ch. 6, Exercise 6) Divide the unit interval [0, 1] into thirds and remove the open interv 1…

A: Given that:   The interval [0,1] is given. divide the [0, 1] into 3 subintervals and delete the open…

Q: 2. Evaluate the following limits. DON'T USE L'HOSPITAL'S RULE IN LIMITS! (a) ( lim√2-2-1 =? (b) lim…

A:

Q: 13. Determine all local maximums and local minimums of the following. (а) х33 — 33х (b) х34 — 34х…

A: In the question we have to calculate local maximum and local minimum for the function given.…

Q: a. The minimum and maximum sıze limits turtles in the legal marine turtle fishery are 40 cm and 60…

A: Given Information :X~N(μ,σ2)μ=55.7σ=11.5

Q: Identify the type of discontinuity at x= - 2. a) Removable Discontinuity b) Essential Jump…

A: The function is said to be continuous at a point if the function holds a definite value in the…

Q: Find global maximum and global minimum of æ3 – 9x? – 48x + 52 on the interval [-5, 12]

A:

Q: 3.3.61 Among all pairs of numbers whose difference is 20, find a pair whose product is as small as…

A: let two number is x and y Their difference is 20

Q: Let A be a positive real number. If the absolute minimum value of f(x) Ar5 35x on [0, oo) occurs at…

A: If the absolute minimum value of f(x)=Ax5-35x3 on [0,∞) occurs at x=cAk. Where A be a positive real…

Q: Use Eceler's formula to express the function:7x) =xarsinx as the sum of a real andd imaginary…

A:

Q: We are building an oblique tower from n pieces of iden- tical, homogeneous blocks on a horizontal…

A: As blocks are identical, the centre of gravity of each block must be at the midpoint. Therefore, the…

Q: Use metaphor/layman's term to describe that Q is dense in R

A:

Q: Assumed that F OG = Ø, show that we can express the infimum and supremum of F NG in terms of the…

A:

Q: Find (with proof) the infimums of the sets S = {1 / n : n  ∈ ℕ} and T = { (-1)n / n : n  ∈ ℕ}. Is…

A:

Q: ,(KGR) ther wise (a) Calculati te pointwise limit fen)alim fca).

A: Given

Q: Graph A polynamyal of even clegree wbose leading 0oefficient is negative, ith 4 real zeos, an…

A: We will use basic concept of polynomials here Even degree means graph is like parabola

Q: Find the absolute minimum valuc, if any, for the function 9 (æ) = a² – 4/T on (0,9] O (9, -15/8) O…

A:

Q: A person in a boat 4 km from the nearest point P on a straight shoreline wants to go to point A on…

A:

Q: 2. ASSume that 9 (x)= 4X-1 of sOme unction gX) the intervaS on which the or.ginal function, 9X), is…

A: Here, the given that the function g(x) has the derivative: g'(x)=4x-1x23

Q: 3. lim (cscx – cotx) X-0+

A:

Q: :IS the urve has ut leas f there is SUCG a vaul ure using for n and ut I thg horozontal asymptotes.…

A: In this question, the concept of asymptote is applied. Asymptote A vertical asymptote is a line that…

Q: 10+ Concave up on the intervalcs): Concauc down on the intervalcsso 4- 6 There is an in flection…

A:

Q: o Using the Formdl definiton of a lime, prove that For) = R is ontinuaus at every paint =X0 that is…

A:

Q: All boxes with a square base, an open top, and a volume of 210 ft cubed have a surface area given by…

A: Approach:As a first step we will differentiate the given function and equate it to zero to find all…

Q: 7. Determine which of the given forms are indeterminate. For each form that is not indeterminate,…

A: Among all given forms, the only indeterminant form is  ∞-∞.

Q: Let A be a positive real number. If the absolute minimum value of f(x) = Ax³ – 90x³ on [0, 00)…

A: we  are given f(x)=Ax5-90x3 and absolute minimum at x=cAk we have to find c?

Q: B. Show directly from the definition (without using Arithmetic of Limits or similar results) that…

A: Let's Solve,

Q: A wire of length 9 is cut into two pieces which are then bent into the shape of a circle of radius r…

A:

Q: 5. Use L'Hôpital's rule to obtain the following limits: (a) lim r²Inr

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

Q: 13. Let P be the perimeter of a rectangular fence. Prove that the shape that encloses the maximum…

A:

Q: 25) Find tue intervel of Canvergencce (e~-sg" :::: (x~3) g fue power seriag n-l n=0 (Be Sure to…

A: Given series is ∑n=0∞(x-3)n-13n-1

Q: --val van. 5. Find the absolute maximum and absolute minimum values of the function f(x) = elgæ) on…

A:

Q: A wire of length 13 is cut into two pieces which are then bent into the shape of a circle of radius…

A:

Q: 2. lim (ex – 1)lnx X0+

A: (2). The given limit is: limx→0+ex-1lnx As we know that, the second indeterminate form is: ±∞±∞ ;…

Q: In an orchestra, 21 people can play stringed instruments, 15 can play brass, and 11 can play…

A: Given 21 people can play stringed instruments 15 can play brass 11 can play percussion 8 performs…

Q: This function: 2. 2 0 4 2 -4 O has a removable discontinuity is continuous has a jump discontinuity…

A: Given: To find the behavior of continuous function.

Q: the campus of a college has plans to construct a rectangular parking lot on land bordered on one…

A:

Q: - Determine Bounded by qucation is the (he the avea the cavue whose +the H-anis 28-1 y -anis and the…

A: Area under the curve y=18-x , x=8 , x-axis and y-axis will be the shaded region in the below graph.…

Q: Make a complete groph of the following funictions, If aninterval is het specified, graphthe…

A:

Q: 53. Show, for f(x) = 3x2 + 4x over [0, 2], that ( 12j², 8j Σ%) RN N2 Then evaluate lim RN.

A:

Q: A wire of length 19 is cut into two pieces which are then bent into the shape of a circle of radius…

A:

Q: e. Find the second derivaitve. f''(x) = f. Use parts b through e to identify maximums as points. g.…

A:

Q: find the value of x at which the polyomial fit y(x) makes the maximum.

A: It is easy to observe the variation in data from the graph of the data. Graph also helps to…

Q: 5. lim 2x-1

A:

Q: Consider the following points. (-1, 4), (0, 0), (1, 1), (4, 58) (a) Determine the polynomlal…

A: The given points are -1, 4, 0, 0, 1, 1 and 4, 58 We have to determine the polynomial function of…

Q: A translation was given by the rule: (x. )-(x-4. 7A point mapped with this rule would have an image…

A: We have to find the rule

Q: Find the minimum value of the expression given below on the horizontal span of 0 to 6.  2x − x2 + 2

A:

Q: Let x and y be two positive numbers. If ry = 75 , find the minimum value of 3x +4y

A: The question mentions that, xy=75 Thus, y=75x Now, let the given function be, S=3x+4y…

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.