find the smallest and largest riemann sum

[kpx001]

given the table
x= -.4, -.2, 0, 0.2, 0.4, 0.6, 0.8
f(x)= 3, 1, 1.5, 2.5, -1, -2, -1.5

find the smallest riemann sum.
find the largest riemann sum.

smallest=[1+1+1.5-1-2-2](6/35) = -.2571 ?
largest=[3+1.5+2.5+2.5-1-1.5](6/35) = 1.2 ?

 

[tkhunny]

It looks like you have the heights correctly determined.

What is 6/35? All your intervals are 0.2 wide.

Note: Please recommend to whoever wrote the question that the language "smallest" and "largest" be changed to "least" and "greatest". Which number is smaller? 6 or 224?

 

[DR._Glockman]

Your number 6 is smaller than your number 224, but your numeral 224 is smaller than your numeral 6.

Merely a question of splitting hairs.

 

[mmm4444bot]

Your number 6 is smaller than your number 224, but your numeral 224 is smaller than your numeral 6.

Merely a question of splitting hairs.

OIC :!:

All numbers are numerals, but not all numerals are numbers, is that it? :twisted:

 

[DR._Glockman]

Numbers are integers, but numerals are symbols for numbers.

Look at it this way: 56 is a number (integer), but it also is the symbol (numeral) for the amount fifty-six.

 

[mmm4444bot]

... Merely a question of splitting hairs.

I agree. (I'm razzing you.)

My dictionary gives 44 definitions for the word "number". The first definition is:

1. a numeral

 

[DR._Glockman]

The difference between numerals and numbers is the same as the difference between words and the things they refer to. A number is a concept that a numeral expresses. The same number can be represented by different numerals. For example, the symbols ‘3’, ‘three’, and ‘III’ are different numerals, but they all represent the same number.

Note: Not my quote, got it off google.

More of splitting hairs: Yes, all numbers are numerals, but the converse isn't necessarily true. For example the symbol for infinity is ? (a numeral), but not a number (where would you put ? on the number line?).

 

[tkhunny]

This discussion has been had many times. It is not splitting hairs and it is not my concern how correct one or the other is or may be. The student could have learned some of the difference between more ambiguity and less ambiguity. There is no "bigger than" symbol.

In any case, the student should learn to strive for more clear language. So also, should problem writers.

 

[mmm4444bot]

... the symbol for infinity is ? (a numeral) ...

Interesting. So, a numeral can possibly represent concepts as well as numbers. Is i a numeral?

... [everyone] should learn to strive for more clear language.

AMEN!

 

[DR._Glockman]

tkhunny was right on this one as it is all a question of semantics. Euler tried to bring the mathematical world into a uniform diction, he was partially sucessful. Does anyone realize that de Carte went to his grave thinking that -8 was greater than -4? On this note I hope this discussion is muted.