Question

For each of the following limits, find the value or explain why it does not exist. (i) (ii) (iii)

a) Limits exist for all
b) Limits exist for some
c) Limits exist for none
d) Insufficient information

Answer 1

Some quantities can be determined exactly, such as the number of seconds in an hour (3600 seconds) and the number of grams in 3 kilograms (3000 grams), while others, like the number of pages in a book, can be counted if the book is present, and the number of grams in one's weight must be measured and is subject to uncertainty.

Step-by-step explanation:

The question asks to indicate whether certain quantities can be determined exactly or must be measured with some degree of uncertainty. For each item listed:

• (a) The number of seconds in an hour can be determined exactly because there are 60 seconds in a minute and 60 minutes in an hour, thus 3600 seconds in an hour.
• (b) The number of pages in a book is a countable quantity. If the book is in front of you and is already printed, then the number of pages can be counted exactly.
• (c) The number of grams in your weight must be measured with some uncertainty as biological weight can fluctuate, and scales may have varying degrees of precision.
• (d) The number of grams in 3 kilograms can be determined exactly because there are 1000 grams in a kilogram, so there are exactly 3000 grams in 3 kilograms.