Let f : R → R be defined by ƒ(0) = 0 and f(x) = sin (±1) for x ± 0. Show that for every c in [−1, 1] there exists a sequence of points x + 0 such that lim→∞ x = 0 and limn→∞ f(x) = c.
Let f : R → R be defined by ƒ(0) = 0 and f(x) = sin (±1) for x ± 0. Show that for every c in [−1, 1] there exists a sequence of points x + 0 such that lim→∞ x = 0 and limn→∞ f(x) = c.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
Question
prove
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
Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage