Show iii. With handwriting solution Let I = (a, b) be a bounded open interval and f:I →R be a monotone increasing function on I.(i) If fƒ is bounded above on I, then lim f(x)sup f(x).x = (a,b)x→6-(ii) If ƒ is bounded below on I, then lim f(x)=inf f(x).ze(a,b)x→a+to∞.(iii) If ƒ is unbounded above on I, then lim f(x)(iv) If ƒ is unbounded below on I, then lim f(x)x→b-xat-∞o.

Answered: Image /qna-images/answer/3f6ffbb4-162d-4d94-aec4-c6ceac20e2d8.jpg

Let I (a, b) be a bounded open interval and f: 1 2 be a monotone increasing function on I. (i) If f is bounded above on I, then lim f(x)= - x468 sup f(x). x= (a,b) lim f(x) inf f(x). - x-at (ii) If f is bounded below on I, then (iii) If f is unbounded above on I, then lim f(x) ∞. ze (a,b) x-6-

Let I (a, b) be a bounded open interval and f: 1 2 be a monotone increasing function on I. (i) If f is bounded above on I, then lim f(x)= - x468 sup f(x). x= (a,b) lim f(x) inf f(x). - x-at (ii) If f is bounded below on I, then (iii) If f is unbounded above on I, then lim f(x) ∞. ze (a,b) x-6-

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

See similar textbooks

Related questions

Q: 12 4 () (23) () (73) 1 1 1 24 24 5

Q: A + ՏԵ + - 2 1}}=?

A: Solution :-

Q: in the magic square so that the sum of the numbers in each row, columm

Q: Find the maximum and minimum values of x^2 + y^2 − 2x − 2y on the disk of radius √ 8 centered at the…

A: Given function is fx,y=x2+y2-2x-2y where bounded region is x2+y2≤8.

Q: Find the probability that. a Family of y children w be at least (1) boy prob

A: Total children in family = 4 the probability of getting 1 boy child is calculated as follows Pat…

Q: Show that the following equation is exact and solve it: (2y sin x cos x - y + 2y² exy²) dx - (x -…

Q: In Exercises 9 to 12, determine whether the two graphs are equivalent. 11. D A B C B A D E F с F E

A: The given problem is related with graph theory. Given two graphs. We have to determine whether the…

Q: 1. Let f(x, y, z) = 9 (√x² + y² + z2²) 7 where g is some nonnegative function of one variable such…

A: Surface is the sphere with radius 2and centre at (0,0,0)

Q: semi-circular baggage compartment in an airplane is 38' long, 15' wide, and 7.5' high. How many…

Q: Use Laplace transform to solve the partial differential equation: d'y dy = -+xt where y(x,0) = 0,…

A: Solution

Q: @ Fs [ f(x)} = - P Fc { fall proof: H.W.

Q: In Exercises 9 to 12, determine whether the two graphs are equivalent. 10. B с A E D C D B E

Q: Find all possible values of a e and Iz+2a-(a + 1)i> 3 simult

Q: Hi the equation for the cone is z^2= x^2 + y^2, and not z=x^2 + y^2, could you please do this…

A: Here we will use Cylindrical co ordinate system x= r cosθ , y = r sinθ , z=zx2+y2=r cosθ2 + r…

Q: Q5) Using graphical method to solve the following matrix game B1 B2 B3 A1 1 3 12 A2 8 6 2

A: This method can only be used in games with no saddle point, and having a pay-off matrix of type n×2…

Q: HOMEWORK 15: Instructions: A. Reduce each equation to a standard form and describe the curve…

A: We can identify the curve from its general equation and then find corresponding points and lines

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A: A connected graph G is said to be Eulerian if the graph G has a Euler circuit. A graph has an Euler…

Q: [(9)se x². d²+xdx + (x²-n²) y=0_ by substitution x== 1102 at 2 pt souhen Hence show that it has no…

Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

Q: radius of convergence is not 1/3. It says 1/3 is incorrect.

A: given series ∑n=1∞2+-1n·x+4n-1 radius of convergence is defined as R=limn→∞12+-1n1n

Q: Find the image of |z + pi + 2p| = 4 under the mapping w = p√² (e¹²) z. about

Q: Use Laplace transform to solve the partial differential equation: o²y_by -+xt where y(x,0) = 0,…

A: Solution

Q: 7. Given f(x) = 6x²+2x-5 and g(x) = 6x²+3x+1. Evaluate (f-g) x.

A: Here given that f(x)=6x2+2x-5 and g(x)=6x2+3x+1 We have…

Q: Consider a triangle ABC, on each of whose sides equilateral triangles are dra

Q: If A = 3ai +4j-k and B = 4i+j-3k, find the value of a if A normal to B.

Q: /Solve the following Assignment problem using the Hungarian method.. 12 3 4 5 J1 83 7 6 2 J2 51 514…

Q: Given: f(x, y) = xy + 8; R is bounded by y = x7.5 and y = 7.5x Question: What is the average…

A: The region bounded by y = x7.5 and y = 7.5x is shown

Q: Solve: y' + 4y - 17y' - 60y: = y(0) = - 4, y'(0) = - -5, y(t) = = - 72et y''(0) = - 65

A: First we will find the Auxiliary equation of given differential equation to get Complementry…

Q: If a, b are complex constants and a real parameter, what does the equation z = a cost+bsint…

Q: Using a binomial approach, find the sum S given by n+1 S="C₁ + "+¹C₁ + "+2² C₂+...+ "*C,

A: Here we can use the following formula to find the sum nCr+nCr+1=n+1Cr+1and nC0=1

Q: Use substitution to find the Taylor series at x = 0 of the function In 1 + 4x8 What is the general…

A: We have to find Taylor series for function in 1+4x8

Q: (ylny - e¯xy)dx + ( + x lny) dy = 0

A: The differential equation Mdx+Ndy=0 is said to be exact differential equation. If it satisfies the…

Q: Exercises: Find the Taylor series for the function at point T a = f(x)= cosx , ● f(x)=√x a = 4 f() =…

Q: Give an example of a non-planar graph that is not contractible to K5or K3,3.

A: Solution :-

Q: Find the basic solution for the following (T. d the optimal solution. 4 1 2 6 9 100 4 3 5 7 120 2 6…

A: Check if the problem is balanced by finding the sum of rows and columns 100+120+120=340…

Q: In Exercises 9 to 12, determine whether the two graphs are equivalent. 10. B с A E D с E D B

Q: Point R has cylindrical coordinates (5,4). Plot R and describe its location in space using…

Q: How many 7-letter words contain exactly 2 vowels? (For example, an 8-letter word with 5 vowels is…

A: To find the number of words contain exactly two vowels :-

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

Q: If ƒ (0) = 1, ƒ (1) = 2, ƒ(2) = 33, f(3) = 244. Find a cubic spline approximation, assuming S" (0) =…

Q: Use Laplace transform to solve the partial differential equation: d²u d²u du(x,0) = t> 0, 0<x<1,…

A: Solution

Q: Find the volume of a right pyramid that has a square base in the xy-plane. − 1 ≤ x ≤ 1, − 1 ≤ y ≤ 1,…

A: Given A right pyramid that has a square base in the xy plane -1<=x <=1 -1<=y <=1…

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A: a) In the graph given in question each vertex has a degree of 4, hence from the Eulerian Graph…

Q: 2. Consider the vector-valued function R(t) = { Show that is continuous at t = 1. (el-¹, 1-², In (2-…

Q: Consider functions f: {1, 2, 3, 4, 5, 6, 7} → {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. a. How many of…

Q: Use Laplace transform to solve the partial differential equation: dy dy +xt where y(x,0)= 0,…

Q: Sum the following series: (a) cosa += cos(a +B) + COS (b) cos(na + B)+cos((n-1)a +2 2 (c) ·cos(α +…

Q: . Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² =…

Q: 7. Evaluate the integral x4 6x5 1 dx

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

Question

Show iii. With handwriting solution

Let I = (a, b) be a bounded open interval and f:I →
R be a monotone increasing function on I.
(i) If fƒ is bounded above on I, then lim f(x)
sup f(x).
x = (a,b)
x→6-
(ii) If ƒ is bounded below on I, then lim f(x)=
inf f(x).
ze(a,b)
x→a+
to
∞.
(iii) If ƒ is unbounded above on I, then lim f(x)
(iv) If ƒ is unbounded below on I, then lim f(x)
x→b-
xat
-∞o.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.
Find an example of a function f : [−1,1] → R such that for A := [0,1], the restrictionf |A(x) → 0 as x → 0, but the limit of f(x) as x → 0 does not exist. Show why
This exercise and the next explore partial converses of the Continuous Limit Theorem (Theorem 6.2.6). Assume fn → f pointwise on [a, b] and the limit function f is continuous on [a, b]. If each fn is increasing (but not necessarily continuous), show fn → f uniformly.
Let f : (0, 1) → R be a differentiable function such that |f'(x)| < 1 for all x ∈ (0, 1). For n ≥ 2 let an = f(1/n ). Show that limn→∞ an exists.
Let a function g be defined on R2 by g(x,y) = (x2yesin(xy^2))/(x2+y2) use g(x,0), g(x,kx), g(x,kx2) , g(ly2,y), where k and l are constants (k =/ 0) and (l =/ 0), and g(rcosθ,rsinθ) to determine if lim(x,y)-->(0,0) g(x,y) exists Also use the squeeze technique to the determine if the limit exists
Given a continuous function f:[0,1]→R, define its sequence of Bernstein polynomials. Please be as clear as possible.
Find an example of a function f:[0,1]→ℝ such that f is not continuous, but f does satisfy the conclusions of the extreme value theorem.
Let g(u) be a differentiable function, and let f(x, y) = g(x^2,y^2) Find the direction of maximal increase of f at the point (1, 1) in termsof g'
determine for which values of x=a the lim f(x) x→a exists but f is not continuous at x=a, and determine for which values of x=a the function is continuous but not differentiable at x=a.
Show that an is decreasing and bounded from below where an+1 = (1+a^2n)/3 and a1 = 1. Then determine lim n→∞ an.
FInd A and B such that g(x) has limits at x= -1 and x=3
(a)Verify the First Mean-Value Theorem for the function g(x)=x^3 +1 on the interval [1,2]. (b) By definition f'(x)= Lim h approaches 0 of {f(x+h)-f(x)/h}. Verify that f'(x)= secx tanx if f(x)= sec x.