1. [Graph]

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

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

asked 2021-09-26

a. Plot the graph of f in the viewing window [0,15] \(\times\) [0,10].

b. Prove that f is increasing on the interval [0, 15].

asked 2021-06-16

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

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 2021-01-25

asked 2021-09-30

One reason for the increase in the life span over the years has been the advances in medical technology. The average life span for American women from Email-trough 2007 is given by \(\displaystyle{W}{\left({t}\right)}={49.9}+{17.1}{\ln{{t}}}{\left({1}\leq{t}\right)}\) where W(t) is measured in years and t is measured in 20-year intervals, with t=1 corresponding to the beginning of 1907.

a. Show that W is increasing on (1, 6).

b. What can you say about the concavity of the graph of W on the interval (1, 6)?

a. Show that W is increasing on (1, 6).

b. What can you say about the concavity of the graph of W on the interval (1, 6)?