Finding Deltas Algebraically Each of Exercises gives a function f(x) and numbers L, c, and e > 0. In each case, find an open interval about c on which the inequal- ity f(x) - L < e holds. Then give a value for 8 > 0 such that for all x satisfying 0 < |x – c| < 8 the inequality |f(x) – L| < ɛ holds. L = 5, L = -6, L = 1, L = 1/2, L = 3. f(x) = x + 1, c = 4, 8 = 0.01 f(x) = 2x – 2, c = -2, 8 = 0.02 f(x) = Vx + 1, c = 0, E = 0.1 f(x) = Vĩ. f(x) = V19 – x, f(x) = Vx – 7. c = 1/4, 8 = 0.1 c = 10, c = 23, 8 = 1 L = 4, f(x) = 1/x, L = 1/4, c = 4, 8 = 0,05

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.3: Getting Information From The Graph Of A Function
Problem 4E: The function f graphed below is defines by a polynomial expression of degree 4. Use the graph to...
icon
Related questions
Question

Each of Exercises gives a function ƒ(x) and numbers L, c, and e 7 0. In each case, find an open interval about c on which the inequality 0 ƒ(x) - L 0 6 e holds. Then give a value for d 7 0 such that for all x satisfying 0 6 0 x - c 0 6 d the inequality 0 ƒ(x) - L 0 6 e holds.

Finding Deltas Algebraically
Each of Exercises
gives a function f(x) and numbers L, c, and
e > 0. In each case, find an open interval about c on which the inequal-
ity f(x) - L < e holds. Then give a value for 8 > 0 such that for all
x satisfying 0 < |x – c| < 8 the inequality |f(x) – L| < ɛ holds.
L = 5,
L = -6,
L = 1,
L = 1/2,
L = 3.
f(x) = x + 1,
c = 4,
8 = 0.01
f(x) = 2x – 2,
c = -2,
8 = 0.02
f(x) = Vx + 1,
c = 0,
E = 0.1
f(x) = Vĩ.
f(x) = V19 – x,
f(x) = Vx – 7.
c = 1/4,
8 = 0.1
c = 10,
c = 23,
8 = 1
L = 4,
f(x) = 1/x,
L = 1/4,
c = 4,
8 = 0,05
Transcribed Image Text:Finding Deltas Algebraically Each of Exercises gives a function f(x) and numbers L, c, and e > 0. In each case, find an open interval about c on which the inequal- ity f(x) - L < e holds. Then give a value for 8 > 0 such that for all x satisfying 0 < |x – c| < 8 the inequality |f(x) – L| < ɛ holds. L = 5, L = -6, L = 1, L = 1/2, L = 3. f(x) = x + 1, c = 4, 8 = 0.01 f(x) = 2x – 2, c = -2, 8 = 0.02 f(x) = Vx + 1, c = 0, E = 0.1 f(x) = Vĩ. f(x) = V19 – x, f(x) = Vx – 7. c = 1/4, 8 = 0.1 c = 10, c = 23, 8 = 1 L = 4, f(x) = 1/x, L = 1/4, c = 4, 8 = 0,05
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Fundamental Theorem
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning