Prove the Limit Statement
-Select the Correct Statement for the Definition

question 199

Multiple Choice

Prove the limit statement
-Select the correct statement for the definition of the limit: $\lim _ { x \rightarrow 0 } f ( x ) = L$ means that___________

• A) if given any number \(\varepsilon > 0\), there exists a number \(\delta > 0\), such that for all \(x\), \(0 < \left| x - x _ { 0 } \right| < \varepsilon\) implies \(| f ( x ) - L | > \delta\).
• B) if given any number \(\varepsilon > 0\), there exists a number \(\delta > 0\), such that for all \(x\), \(0 < \left| x - x _ { 0 } \right| < \varepsilon\) implies \(| f ( x ) - L | < \delta\).
• C) if given a number \(\varepsilon > 0\), there exists a number \(\delta > 0\), such that for all \(x\), \(0 < \left| x - x _ { 0 } \right| < \delta\) implies \(| f ( x ) - L | > \varepsilon\).
• D) if given any number \(\varepsilon > 0\), there exists a number \(\delta > 0\), such that for all \(x\), \(0 < \left| x - x _ { 0 } \right| < \delta\) implies \(| f ( x ) - L | < \varepsilon\).

---

Definitions:

Schizophrenia

A mental disorder characterized by delusions, hallucinations, disorganized speech, and significant social or occupational dysfunction.

Nerve Pathways

The routes taken by nerve impulses as they move through the body's nervous system.

Animal Studies

Research conducted on non-human animals to gain insights into biology, behavior, diseases, and the testing of drugs or procedures for human application.

Milieu Therapy

A therapeutic approach that utilizes the social environment of a patient, such as a psychiatric hospital or community setting, to promote healing and change.