Answered: Question 4 Which among the choices is… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

See similar textbooks

Related questions

Question

Question 4
Which among the choices is not true about the continuity of f(x)?
if x < 0
if 0 ≤ x ≤ 1
if x > 1
f(x) =
X,
x²,
(2 - x),
Of(x) is continuous
O f(1) = 1
O There is a finite-jump discontinuity at x = 1
Olim, →₁¹ f(x) = 1

Expert Solution

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
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.
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.
1. a. Suppose F is of bounded variation on [a,b], then |F'| = VF' a.e b. F is absolute continuous if and only if VF is absolute continuous on [a,b]
Is the proof correct? Either state that it is, or circle the first error and explain what isincorrect about it. If the proof is not correct, can it be fixed to prove the claim true?Claim:If f : (0, 1] → R and g : [1, 2) → R are uniformly continuous on their domains, andf(1) = g(1), then the function h : (0, 2) → R, defined by h(x) = f(x) for x ∈ (0, 1] g(x) for x ∈ [1, 2),is uniformly continuous on (0, 2).Proof:Let e > 0.Since f is uniformly continuous on (0, 1], there exists δ1 > 0 such that if x, y ∈ (0, 1] and|x − y| < δ1, then |f(x) − f(y)| < e/2.Since g is uniformly continuous on [1, 2), there exists δ2 > 0 such that if x, y ∈ [1, 2) and|x − y| < δ2, then |g(x) − g(y)| < e/2.Let δ = min{δ1, δ2}.Now suppose x, y ∈ (0, 2) with x < y and |x − y| < δ.If x, y ∈ (0, 1], then |x − y| < δ ≤ δ1 and so |h(x) − h(y)| = |f(x) − f(y)| < e/2 < e.If x, y ∈ [1, 2), then |x − y| < δ ≤ δ2 and so |h(x) − h(y)| = |g(x) − g(y)| < e/2 < e.If x ∈…
8 Examine holomorphism of given function f(z) = |z|2
Suppose f is differentiable on (0,1) and that there exists M > 0 so that|f′(x)|≤M for all x ∈(0,1).Prove that f is uniformly continuous on (0,1).
True or False A function f has a local maximum at c if there is an open interval I containing c such that for all x in I, f(x) <=f(c).
A function f:D→ℝ is said to have a local maximum [respectively, minimum] at a point x0∈D if there exists a neighborhood U of x0 such that f(x)≤f(x0) [respectively, f(x)≥f(x0)] for all x∈U∩D.Suppose for some integer n≥2 that the derivatives f′,f′′,...,f(n) exist and are continuous on an open interval I containing x0 and that f′(x0)=...=f(n-1)(x0)=0, but f(n)(x0)≠0. Use Taylor's theorem to prove:(b) If n is even and f(n)(x0)>0, then f has a local minimum at x0. (c) If n is odd, then f has neither a local maximum nor a local minimum at x0.

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

College Algebra

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

College Algebra

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

College Algebra (MindTap Course List)

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS