Basic Technical Mathematics
11th Edition
ISBN: 9780134437705
Author: Washington
Publisher: PEARSON
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Chapter 27.7, Problem 1PE
To determine
The value of
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Could you please answer this question using excel.Thanks
1. Calculate the integral
500
x sin x
(a² +x2)20
dx
by using the residue theorem. You may assume that a is real and a > 0. Your solution should
clearly explain the closed contour you are using, and state clearly any vanishing properties
of integrals over contours that are being used.
Questions
An insurance company's cumulative incurred claims for the last 5 accident years are given
in the following table:
Development Year
Accident Year 0
2018
1 2 3 4
245 267 274 289 292
2019
255 276 288 294
2020
265 283 292
2021
263 278
2022
271
It can be assumed that claims are fully run off after 4 years. The premiums received for
each year are:
Accident Year Premium
2018
306
2019
312
2020
318
2021
326
2022
330
You do not need to make any allowance for inflation.
1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method.
(b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method.
2. Comment on the differences in the reserves produced by the methods in Part 1.
Chapter 27 Solutions
Basic Technical Mathematics
Ch. 27.1 - Prob. 1PECh. 27.1 - Prob. 2PECh. 27.1 - Prob. 1ECh. 27.1 - Prob. 2ECh. 27.1 - Prob. 3ECh. 27.1 - Prob. 4ECh. 27.1 - Prob. 5ECh. 27.1 - Prob. 6ECh. 27.1 - Prob. 7ECh. 27.1 - Prob. 8E
Ch. 27.1 - Prob. 9ECh. 27.1 - Prob. 10ECh. 27.1 - Prob. 11ECh. 27.1 - Prob. 12ECh. 27.1 - Prob. 13ECh. 27.1 - Prob. 14ECh. 27.1 - Prob. 15ECh. 27.1 - Prob. 16ECh. 27.1 - Prob. 17ECh. 27.1 - Prob. 18ECh. 27.1 - Prob. 19ECh. 27.1 - Prob. 20ECh. 27.1 - Prob. 21ECh. 27.1 - Prob. 22ECh. 27.1 - Prob. 23ECh. 27.1 - Prob. 24ECh. 27.1 - Prob. 25ECh. 27.1 - In Exercises 3–34, find the derivatives of the...Ch. 27.1 - Prob. 27ECh. 27.1 - Prob. 28ECh. 27.1 - Prob. 29ECh. 27.1 - Prob. 30ECh. 27.1 - Prob. 31ECh. 27.1 - Prob. 32ECh. 27.1 - Prob. 33ECh. 27.1 - Prob. 34ECh. 27.1 - Prob. 35ECh. 27.1 - Prob. 36ECh. 27.1 - Prob. 37ECh. 27.1 - Prob. 38ECh. 27.1 - Prob. 39ECh. 27.1 - Prob. 40ECh. 27.1 - Prob. 41ECh. 27.1 - Prob. 42ECh. 27.1 - Prob. 43ECh. 27.1 - Prob. 44ECh. 27.1 - Prob. 45ECh. 27.1 - Prob. 46ECh. 27.1 - Prob. 47ECh. 27.1 - Prob. 48ECh. 27.1 - Prob. 49ECh. 27.1 - Prob. 50ECh. 27.1 - Prob. 51ECh. 27.1 - Prob. 52ECh. 27.1 - Prob. 53ECh. 27.1 - Prob. 54ECh. 27.1 - The blade of a saber saw moves vertically up and...Ch. 27.1 - Prob. 56ECh. 27.1 - Prob. 57ECh. 27.1 - Prob. 58ECh. 27.1 - Prob. 59ECh. 27.1 - Prob. 60ECh. 27.2 - Prob. 1PECh. 27.2 - Prob. 2PECh. 27.2 - Prob. 1ECh. 27.2 - Prob. 2ECh. 27.2 - Prob. 3ECh. 27.2 - Prob. 4ECh. 27.2 - Prob. 5ECh. 27.2 - Prob. 6ECh. 27.2 - Prob. 7ECh. 27.2 - Prob. 8ECh. 27.2 - Prob. 9ECh. 27.2 - Prob. 10ECh. 27.2 - Prob. 11ECh. 27.2 - Prob. 12ECh. 27.2 - Prob. 13ECh. 27.2 - Prob. 14ECh. 27.2 - Prob. 15ECh. 27.2 - Prob. 16ECh. 27.2 - Prob. 17ECh. 27.2 - Prob. 18ECh. 27.2 - Prob. 19ECh. 27.2 - Prob. 20ECh. 27.2 - Prob. 21ECh. 27.2 - Prob. 22ECh. 27.2 - Prob. 23ECh. 27.2 - Prob. 24ECh. 27.2 - Prob. 25ECh. 27.2 - Prob. 26ECh. 27.2 - Prob. 27ECh. 27.2 - Prob. 28ECh. 27.2 - Prob. 29ECh. 27.2 - Prob. 30ECh. 27.2 - Prob. 31ECh. 27.2 - Prob. 32ECh. 27.2 - Prob. 33ECh. 27.2 - In Exercises 3–34, find the derivatives of the...Ch. 27.2 - Prob. 35ECh. 27.2 - Prob. 36ECh. 27.2 - Prob. 37ECh. 27.2 - Prob. 38ECh. 27.2 - Prob. 39ECh. 27.2 - Prob. 40ECh. 27.2 - Prob. 41ECh. 27.2 - Prob. 42ECh. 27.2 - Prob. 43ECh. 27.2 - Prob. 44ECh. 27.2 - Prob. 45ECh. 27.2 - Prob. 46ECh. 27.2 - Prob. 47ECh. 27.2 - Prob. 48ECh. 27.2 - Prob. 49ECh. 27.2 - Prob. 50ECh. 27.2 - Prob. 51ECh. 27.2 - Prob. 52ECh. 27.2 - Prob. 53ECh. 27.2 - Prob. 54ECh. 27.3 - Prob. 1PECh. 27.3 - Prob. 2PECh. 27.3 - Prob. 1ECh. 27.3 - Prob. 2ECh. 27.3 - Prob. 3ECh. 27.3 - Prob. 4ECh. 27.3 - Prob. 5ECh. 27.3 - Prob. 6ECh. 27.3 - Prob. 7ECh. 27.3 - Prob. 8ECh. 27.3 - Prob. 9ECh. 27.3 - Prob. 10ECh. 27.3 - Prob. 11ECh. 27.3 - Prob. 12ECh. 27.3 - Prob. 13ECh. 27.3 - Prob. 14ECh. 27.3 - Prob. 15ECh. 27.3 - Prob. 16ECh. 27.3 - Prob. 17ECh. 27.3 - Prob. 18ECh. 27.3 - Prob. 19ECh. 27.3 - Prob. 20ECh. 27.3 - Prob. 21ECh. 27.3 - Prob. 22ECh. 27.3 - Prob. 23ECh. 27.3 - Prob. 24ECh. 27.3 - Prob. 25ECh. 27.3 - Prob. 26ECh. 27.3 - Prob. 27ECh. 27.3 - Prob. 28ECh. 27.3 - Prob. 29ECh. 27.3 - Prob. 30ECh. 27.3 - Prob. 31ECh. 27.3 - Prob. 32ECh. 27.3 - Prob. 33ECh. 27.3 - Prob. 34ECh. 27.3 - Prob. 35ECh. 27.3 - Prob. 36ECh. 27.3 - Prob. 37ECh. 27.3 - Prob. 38ECh. 27.3 - Prob. 39ECh. 27.3 - Prob. 40ECh. 27.3 - Prob. 41ECh. 27.3 - Prob. 42ECh. 27.3 - Prob. 43ECh. 27.3 - Prob. 44ECh. 27.3 - Prob. 45ECh. 27.3 - Prob. 46ECh. 27.3 - Prob. 47ECh. 27.3 - Prob. 48ECh. 27.3 - Prob. 49ECh. 27.3 - Prob. 50ECh. 27.3 - Prob. 51ECh. 27.3 - Prob. 52ECh. 27.3 - Prob. 53ECh. 27.3 - Prob. 54ECh. 27.4 - Prob. 1PECh. 27.4 - Prob. 1ECh. 27.4 - Prob. 2ECh. 27.4 - Prob. 3ECh. 27.4 - Prob. 4ECh. 27.4 - Prob. 5ECh. 27.4 - Prob. 6ECh. 27.4 - Prob. 7ECh. 27.4 - Prob. 8ECh. 27.4 - Prob. 9ECh. 27.4 - Prob. 10ECh. 27.4 - Prob. 11ECh. 27.4 - Prob. 12ECh. 27.4 - In Exercises 3–40, solve the given...Ch. 27.4 - Prob. 14ECh. 27.4 - Prob. 15ECh. 27.4 - Prob. 16ECh. 27.4 - Prob. 17ECh. 27.4 - In Exercises 3–40, solve the given...Ch. 27.4 - Prob. 19ECh. 27.4 - Prob. 20ECh. 27.4 - Prob. 21ECh. 27.4 - Prob. 22ECh. 27.4 - Prob. 23ECh. 27.4 - Prob. 24ECh. 27.4 - Prob. 25ECh. 27.4 - Prob. 26ECh. 27.4 - Prob. 27ECh. 27.4 - Prob. 28ECh. 27.4 - Prob. 29ECh. 27.4 - Prob. 30ECh. 27.4 - Prob. 31ECh. 27.4 - Prob. 32ECh. 27.4 - Prob. 33ECh. 27.4 - Prob. 34ECh. 27.4 - Prob. 35ECh. 27.4 - Prob. 37ECh. 27.4 - Prob. 39ECh. 27.4 - Prob. 40ECh. 27.5 - Prob. 1PECh. 27.5 - Prob. 2PECh. 27.5 - Prob. 1ECh. 27.5 - Prob. 2ECh. 27.5 - Prob. 3ECh. 27.5 - Prob. 4ECh. 27.5 - Prob. 5ECh. 27.5 - Prob. 6ECh. 27.5 - Prob. 7ECh. 27.5 - Prob. 8ECh. 27.5 -
In Exercises 3–34, find the derivatives of the...Ch. 27.5 - Prob. 10ECh. 27.5 - Prob. 11ECh. 27.5 - Prob. 12ECh. 27.5 - Prob. 13ECh. 27.5 - Prob. 14ECh. 27.5 - Prob. 15ECh. 27.5 - Prob. 16ECh. 27.5 - Prob. 17ECh. 27.5 - Prob. 18ECh. 27.5 - Prob. 19ECh. 27.5 - Prob. 20ECh. 27.5 - Prob. 21ECh. 27.5 - Prob. 22ECh. 27.5 - Prob. 23ECh. 27.5 - Prob. 24ECh. 27.5 - Prob. 25ECh. 27.5 - Prob. 26ECh. 27.5 - Prob. 27ECh. 27.5 - Prob. 28ECh. 27.5 - Prob. 29ECh. 27.5 - Prob. 30ECh. 27.5 - Prob. 31ECh. 27.5 - Prob. 32ECh. 27.5 - Prob. 33ECh. 27.5 - Prob. 34ECh. 27.5 - Prob. 35ECh. 27.5 - Prob. 36ECh. 27.5 - Prob. 37ECh. 27.5 - Prob. 38ECh. 27.5 - Prob. 39ECh. 27.5 - Prob. 40ECh. 27.5 - Prob. 41ECh. 27.5 - Prob. 42ECh. 27.5 - Prob. 43ECh. 27.5 - Prob. 44ECh. 27.5 - Prob. 45ECh. 27.5 - Prob. 46ECh. 27.5 - Prob. 47ECh. 27.5 - Prob. 48ECh. 27.5 - Prob. 49ECh. 27.5 - Prob. 50ECh. 27.5 - Prob. 51ECh. 27.5 - Prob. 52ECh. 27.5 - Prob. 53ECh. 27.5 - Prob. 54ECh. 27.5 - Prob. 55ECh. 27.5 - Prob. 56ECh. 27.6 - Prob. 1PECh. 27.6 - Prob. 2PECh. 27.6 - Prob. 1ECh. 27.6 - Prob. 2ECh. 27.6 - Prob. 3ECh. 27.6 - Prob. 4ECh. 27.6 - Prob. 5ECh. 27.6 - Prob. 6ECh. 27.6 - Prob. 7ECh. 27.6 - Prob. 8ECh. 27.6 - Prob. 9ECh. 27.6 - Prob. 10ECh. 27.6 - Prob. 11ECh. 27.6 - Prob. 12ECh. 27.6 - Prob. 13ECh. 27.6 - Prob. 14ECh. 27.6 - Prob. 15ECh. 27.6 - Prob. 16ECh. 27.6 - Prob. 17ECh. 27.6 - Prob. 18ECh. 27.6 - Prob. 19ECh. 27.6 - Prob. 20ECh. 27.6 - Prob. 21ECh. 27.6 - Prob. 22ECh. 27.6 - Prob. 23ECh. 27.6 - Prob. 24ECh. 27.6 - Prob. 25ECh. 27.6 - Prob. 26ECh. 27.6 - Prob. 27ECh. 27.6 - Prob. 28ECh. 27.6 - Prob. 29ECh. 27.6 - Prob. 30ECh. 27.6 - Prob. 31ECh. 27.6 - Prob. 32ECh. 27.6 - Prob. 33ECh. 27.6 - Prob. 34ECh. 27.6 - Prob. 35ECh. 27.6 - Prob. 36ECh. 27.6 - Prob. 37ECh. 27.6 - Prob. 38ECh. 27.6 - Prob. 39ECh. 27.6 - Prob. 40ECh. 27.6 - Prob. 41ECh. 27.6 - Prob. 42ECh. 27.6 - Prob. 43ECh. 27.6 - Prob. 44ECh. 27.6 - Prob. 45ECh. 27.6 - In Exercises 33–54, solve the given...Ch. 27.6 - Prob. 47ECh. 27.6 - Prob. 48ECh. 27.6 - Prob. 49ECh. 27.6 - Prob. 50ECh. 27.6 - Prob. 51ECh. 27.6 - Prob. 52ECh. 27.6 - Prob. 53ECh. 27.6 - Prob. 54ECh. 27.6 - Prob. 55ECh. 27.6 - Prob. 56ECh. 27.7 - Prob. 1PECh. 27.7 - Prob. 2PECh. 27.7 - Prob. 1ECh. 27.7 - Prob. 2ECh. 27.7 - Prob. 3ECh. 27.7 - Prob. 4ECh. 27.7 - In Exercises 3–36, evaluate each limit (if it...Ch. 27.7 - Prob. 6ECh. 27.7 - Prob. 7ECh. 27.7 - Prob. 8ECh. 27.7 - Prob. 9ECh. 27.7 - Prob. 10ECh. 27.7 - Prob. 11ECh. 27.7 - Prob. 12ECh. 27.7 - Prob. 13ECh. 27.7 - Prob. 14ECh. 27.7 - Prob. 15ECh. 27.7 - Prob. 16ECh. 27.7 - Prob. 17ECh. 27.7 - Prob. 18ECh. 27.7 - Prob. 19ECh. 27.7 - Prob. 20ECh. 27.7 - Prob. 21ECh. 27.7 - Prob. 22ECh. 27.7 - Prob. 23ECh. 27.7 - Prob. 24ECh. 27.7 - Prob. 25ECh. 27.7 - Prob. 26ECh. 27.7 - Prob. 27ECh. 27.7 - Prob. 28ECh. 27.7 - Prob. 29ECh. 27.7 - In Exercises 3–36, evaluate each limit (if it...Ch. 27.7 - Prob. 31ECh. 27.7 - Prob. 32ECh. 27.7 - Prob. 33ECh. 27.7 - Prob. 34ECh. 27.7 - Prob. 35ECh. 27.7 - Prob. 36ECh. 27.7 - Prob. 37ECh. 27.7 - Prob. 38ECh. 27.7 - Prob. 39ECh. 27.7 - Prob. 40ECh. 27.7 - Prob. 41ECh. 27.7 - Prob. 42ECh. 27.7 - Prob. 43ECh. 27.7 - Prob. 44ECh. 27.7 - Prob. 45ECh. 27.7 - Prob. 46ECh. 27.7 - Prob. 47ECh. 27.7 - Prob. 48ECh. 27.8 - Prob. 1PECh. 27.8 - In Exercises 1 and 2, make the given changes in...Ch. 27.8 - Prob. 2ECh. 27.8 - In Exercises 3–14, sketch the graphs of the given...Ch. 27.8 - Prob. 4ECh. 27.8 - In Exercises 3–14, sketch the graphs of the given...Ch. 27.8 - Prob. 6ECh. 27.8 - Prob. 7ECh. 27.8 - Prob. 8ECh. 27.8 - Prob. 9ECh. 27.8 - Prob. 10ECh. 27.8 - Prob. 11ECh. 27.8 - In Exercises 3–14, sketch the graphs of the given...Ch. 27.8 - Prob. 13ECh. 27.8 - Prob. 14ECh. 27.8 - Prob. 15ECh. 27.8 - Prob. 16ECh. 27.8 - Prob. 17ECh. 27.8 - Prob. 18ECh. 27.8 - Prob. 19ECh. 27.8 - Prob. 20ECh. 27.8 - Prob. 21ECh. 27.8 - Prob. 22ECh. 27.8 - Prob. 23ECh. 27.8 - Prob. 25ECh. 27.8 - Prob. 26ECh. 27.8 - Prob. 27ECh. 27.8 - Prob. 28ECh. 27.8 - Prob. 29ECh. 27.8 - Prob. 30ECh. 27.8 - Prob. 31ECh. 27.8 - Prob. 32ECh. 27.8 - Prob. 33ECh. 27.8 - Prob. 34ECh. 27.8 - The energy E (in J) dissipated by a certain...Ch. 27.8 - Prob. 36ECh. 27.8 - Prob. 37ECh. 27.8 - Prob. 39ECh. 27.8 - A package of weather instruments is propelled into...Ch. 27.8 - Prob. 41ECh. 27.8 - Prob. 42ECh. 27.8 - Prob. 43ECh. 27.8 - Prob. 45ECh. 27.8 - Prob. 46ECh. 27 - Prob. 1RECh. 27 - Prob. 2RECh. 27 - Prob. 3RECh. 27 - Prob. 4RECh. 27 - Prob. 5RECh. 27 - Prob. 6RECh. 27 - Prob. 7RECh. 27 - Prob. 8RECh. 27 - Prob. 9RECh. 27 - Prob. 10RECh. 27 - Prob. 11RECh. 27 - Prob. 12RECh. 27 - Prob. 13RECh. 27 - Prob. 14RECh. 27 - Prob. 15RECh. 27 - Prob. 16RECh. 27 - Prob. 17RECh. 27 - Prob. 18RECh. 27 - Prob. 19RECh. 27 - Prob. 20RECh. 27 - Prob. 21RECh. 27 - Prob. 22RECh. 27 - Prob. 23RECh. 27 - Prob. 24RECh. 27 - Prob. 25RECh. 27 - Prob. 26RECh. 27 - Prob. 27RECh. 27 - Prob. 28RECh. 27 - Prob. 29RECh. 27 - Prob. 30RECh. 27 - Prob. 31RECh. 27 - Prob. 32RECh. 27 - Prob. 33RECh. 27 - Prob. 34RECh. 27 - Prob. 35RECh. 27 - 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