Use the Squeeze Theorem to show that lim x→0 x2 cos(16?x) = 0.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 15T
Related questions
Question
A graphing calculator is recommended.
Use the Squeeze Theorem to show that
lim x→0 x2 cos(16?x) = 0.
Illustrate by graphing the functions
f(x) = −x2,
g(x) = x2 cos(16?x),
and
h(x) = x2
on the same screen.Let
f(x) = −x2, g(x) = x2 cos(16?x),
and
h(x) = x2.
Then
≤ cos(16?x) ≤
⇒
≤ x2 cos(16?x) ≤ .
Since
lim x→0 f(x) = lim x→0 h(x) = ,
by the Squeeze Theorem we have
lim x→0 g(x) = .
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning