We appreciate your visit to Self paced Calculus 1 Fall 2021 Homework 2 2 unit 1 a It can be shown that the inequalities 1 2 b Graph 1 2. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
In this problem, we are given the inequality 1 - 2|a| ≤ 0. We need to determine if this inequality holds for all values of a close to zero and discuss what this tells us about the behavior of the function sin(x) - 2x.
The given inequality is 1 - 2|a| ≤ 0. To analyze the behavior of this inequality as a approaches zero, we consider two cases: a > 0 and a < 0.
Case a > 0:
In this case, the inequality becomes 1 - 2a ≤ 0. Solving for a, we get a ≤ 1/2. As a approaches zero from the positive side, a ≤ 1/2 still holds true.
Case a < 0:
In this case, the inequality becomes 1 + 2a ≤ 0. Solving for a, we get a ≤ -1/2. As a approaches zero from the negative side, a ≤ -1/2 still holds true.
Therefore, for all values of a close to zero, the inequality 1 - 2|a| ≤ 0 holds true.
Now, considering the behavior of the function f(x) = sin(x) - 2x, we can conclude that as x approaches zero, the function approaches zero or remains bounded.
This is because the inequality holds for all values of a close to zero, indicating that the function sin(x) - 2x does not cross the x-axis near x = 0.
In summary, the given inequality 1 - 2|a| ≤ 0 holds for all values of a close to zero, which tells us that the function sin(x) - 2x does not cross the x-axis near x = 0.
To learn more about, inequality:-
brainly.com/question/25944814
#SPJ11
Thanks for taking the time to read Self paced Calculus 1 Fall 2021 Homework 2 2 unit 1 a It can be shown that the inequalities 1 2 b Graph 1 2. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
