1. [Graph]

2. We substitute \(t=1\) (any number from (0,15)) into f'(t)'

\(\displaystyle{f}'{\left({1}\right)}=-{\frac{{{1341}\dot{{1}}^{{{2}}}-{19728}\dot{{1}}-{5192}}}{{{100000}}}}={0.23578}\)

Question

asked 2021-06-16

asked 2021-06-23

You were asked about advantages of using box plots and dot plots to describe and compare distributions of scores. Do you think the advantages you found would exist not only for these data, but for numerical data in general? Explain.

asked 2021-05-05

The following advanced exercise use a generalized ratio test to determine convergence of some series that arise in particular applications, including the ratio and root test, are not powerful enough to determine their convergence. The test states that if $$ \(\displaystyle\lim{\left\lbrace{n}\rightarrow\infty\right\rbrace}{\frac{{{a}{\left\lbrace{2}{n}\right\rbrace}}}{{{a}_{{{n}}}}}}{<}\frac{{1}}{{2}}\) then \(\sum a_{n} \)converges,while if \(\displaystyle\lim{\left\lbrace{n}\rightarrow\infty\right\rbrace}{\frac{{{a}{\left\lbrace{2}{n}+{1}\right\rbrace}}}{{{a}_{{{n}}}}}}{>}\frac{{1}}{{2}}\), then \(\sum a_{n}\) diverges.

Let \(\displaystyle{a}_{{{n}}}={\frac{{{1}}}{{{1}+{x}}}}{\frac{{{2}}}{{{2}+{x}}}}\ldots{\frac{{{n}}}{{{n}+{x}}}}{\frac{{{1}}}{{{n}}}}={\frac{{{\left({n}-{1}\right)}!}}{{{\left({1}+{x}\right)}{\left({2}+{x}\right)}\ldots{\left({n}+{x}\right)}}}}\).

Show that \(\frac{a_{2 n}}{a_{n}} \leq \frac{e^{-x / 2}}{2}\) . For which x > 0 does the generalized ratio test imply convergence of \(\sum_{n=1}^\infty a_{n}\)?

asked 2021-05-05