Provide an appropriate response.(a) Show that  converges.(b) Show that  ? 0.0002.(c) Suppose  is approximated by . Based on your answer to part (b), what is the maximum possible error?(d) Use a numerical method to estimate the value of .(e) Determine

whether  converges or diverges, and justify  your answer. If it converges, estimate its value to an accuracy of at  least two decimal places.



What will be an ideal response?


(a)Possible answer:
 Note that  =  + .
 Since  is a proper integral and  converges 
 by direct comparison to  converges.
(b)  ?  = 0.0002.
(c) 0.0002
(d) 1.209
(e) diverges

Mathematics

You might also like to view...

Determine convergence or divergence of the alternating series.

A. Diverges B. Converges

Mathematics

Simplify the expression.3x + 1 + 7x + 12

A. 10x + 13 B. 21x + 13 C. 20x D. 10x

Mathematics

Use transformations to explain how the graph of the given function can be obtained from the graph of the appropriate root function (y =  or y =).y =  + 10

A. Shift the graph of y =  to the left 10 units and downward 8 units.
B. Shift the graph of y =  to the right 10 units and upward 8 units.
C. Shift the graph of y =  to the left 8 units and downward 10 units.
D. Shift the graph of y =  to the right 8 units and upward 10 units.

Mathematics

Solve the problem.In the formula N = Iekt, N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time. How long will it take for the population of a certain country to triple if its annual growth rate is 0.5%? Round to the nearest year.

A. 1 yr B. 95 yr C. 600 yr D. 220 yr

Mathematics