Provide an Appropriate Response $\lim _ { \mathrm { n } \rightarrow\infty } \frac { \ln \mathrm { n } } { \mathrm { n } ^ { \mathrm { c } } } = 0$

question 13

Multiple Choice

Provide an appropriate response.
-It can be shown that $\lim _ { \mathrm { n } \rightarrow\infty } \frac { \ln \mathrm { n } } { \mathrm { n } ^ { \mathrm { c } } } = 0$ for $\mathrm { c } > 0$ . Find the smallest value of $\mathrm { N }$ such that $\left| \frac { \ln \mathrm { n } } { \mathrm { n } ^ { \mathrm { c } } } \right| < \varepsilon$ for all $\mathrm { n } > \mathrm { N }$ if $\varepsilon = 0.01$ and $c = 1.8$ .

• A) 35
• B) 25
• C) 28
• D) 31

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Definitions:

Nuclear Medicine Scan

A diagnostic imaging technique using small amounts of radioactive material to diagnose or treat diseases.

Radionuclide Imaging

A medical imaging technique that involves the use of radioactive substances to diagnose or treat diseases.

Radionuclides

Radioactive isotopes of elements, used in medical diagnostics, treatment, and research for their ability to emit radiation.

Radioisotopes

Radioactive isotopes that emit radiation and are used in medical diagnostics, treatment, and various types of research.