Exam 16: Series and Taylor Polynomials Web

Suppose the ratio $a _ { n }$ of alligators to pythons in a marshland from 2001 to 2008 can be approximated by the model $a _ { n } = 24 - 3.5 n + 0.34 n ^ { 2 }$ $n = 1,2 , \mathrm {~K} , 8$ where $n$ is the year, with $n = 1,2 , \mathrm {~K} , 8$ corresponding to $2001,2002 , \mathrm {~K} , 2008$ In 2006, the total number of alligators and pythons in the marsh was about 900. In that year, how many were pythons?

The annual sales $a _ { n }$ (in millions of dollars) for a certain company from 2001 to 2006 can be approximated by the model $a _ { n } = 500.7 + 161.52 n,$ $n = 0,1 , K , 5$ where $n$ represents the year, with $n = 0$ corresponding to 2001. Find the total sales from 2001 to 2004. Round to the nearest million.

Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that n begins with 1.) $a _ { n } = - 8 \left( \frac { 1 } { 5 } \right) ^ { n }$

Use Newton's Method to approximate $\sqrt [ 4 ] { 6 }$ . Round your answer to three decimal places.

Determine whether the sequence is geometric. If so, find the common ratio. 5, 7, 9, 11, ...

Find the radius of convergence of the series $\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n + 4 } ( x - 8 ) ^ { n + 4 } } { n + 4 }$ .

Use Newton's Method to find the point on the graph of $f ( x ) = 4 - x ^ { 2 }$ that is closest to the point $( 1,0 )$ . Round your answer to three decimal places.

Use Newton's Method to approximate the x-value of the indicated point intersection of the two graphs accurate to three decimal places. f(x)=2x+1 g(x)=

Use the fourth-degree Taylor polynomial centered at c = 2 for the function $f ( x ) = \ln x$ to approximate $f \left( \frac { 3 } { 2 } \right)$ . Round your answer to nearest ten thousandth.

Write an expression for the nth term of the sequence 2, 8, 26, 80, ....

Determine whether the sequence is geometric. If so, find the common ratio. 1, -3, 9, -27, ...

Write the first five terms of the arithmetic sequence. $a _ { 5 } = 19 , a _ { 15 } = 79$

Write the first five terms of the sequence. an = $\left( - \frac { 5 } { 6 } \right) ^ { n }$

Find the radius of convergence of the power series. $\sum _ { n = 0 } ^ { \infty } \frac { ( 5 x ) ^ { 2 n } } { ( 2 n ) ! }$

Consider a job offer with a starting salary of $43,200 and a given annual raise of $2175. Determine the total compensation from the company through seven full years of employment.

Match the arithmetic sequence with its graph from the choices below. $a _ { n } = 35 - 3 n$

Find the power series for the function $f ( x ) = e ^ { x ^ { 8 } }$ using the power series for $e ^ { x }$ .

The annual spending by tourists in a resort city is 200 million dollars. Approximately 75% of that revenue is again spent in the resort city, and of that amount approximately 75% is again spent in the resort city. If this pattern continues, write the geometric series that gives the total amount of spending generated by the 200 million dollars (including the initial outlay of 200 million dollars) and find the sum of the series.

Find the sum. $\sum _ { i = 1 } ^ { 3 } ( 3 i - 5 )$

Find the radius of convergence of the power series. $\sum _ { n = 1 } ^ { \infty } \frac { ( x - 6 ) ^ { n - 1 } } { 6 ^ { n - 1 } }$