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### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

# Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counter example.(a) True or False: The n-rectangle lower sum for f on [a, b] is always equal to the corresponding right sum.

The given statement is False

See the step by step solution

## Step 1: Given Information

The $n-$Rectangle lower sum for $f$ on $\left[a,b\right]$ is always equal to the corresponding right sum.

## Step 2: Calculation

The statement is,
The $n-$Rectangle lower sum for $f$ on $\left[a,b\right]$is always equal to the corresponding right sum.
The statement is false.The upper sum is always greater than or equal to the actual signed area where as the lower sum is always less than or equal to the actual signed area.Therefore, the statement is false

## Step 3: Conclusion

Therefore, the given statement is false

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