(a) Estimate the area under the graph of f(x) = 4/x from x = 1 to x = 5 using four approximating rectangles and right endpoints. R4 = (b) Repeat part (a) using left endpoints. L4 = (c) By looking at a sketch of the graph and the rectangles, determine for each estimate whether is overestimates, underestimates, or is the exact area. Underestimate 1. L4 2. R4 Exact

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter58: Achievement Review—section Five
Section: Chapter Questions
Problem 30AR: Determine dimension x to 3 decimal places.
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### Estimating the Area under a Curve

#### (a) Estimate the Area Using Right Endpoints

To estimate the area under the graph of \( f(x) = \frac{4}{x} \) from \( x = 1 \) to \( x = 5 \) using four approximating rectangles and right endpoints:

\[ R_4 = \]

#### (b) Repeat the Estimation Using Left Endpoints

To estimate the area under the same graph using left endpoints:

\[ L_4 = \]

#### (c) Determine the Accuracy of Each Estimate

By looking at a sketch of the graph and the rectangles, determine for each estimate whether it is an overestimate, underestimate, or the exact area.

**Underestimate** 
\[ 1. \quad L_4 \]

**Exact** 
\[ 2. \quad R_4 \]
Transcribed Image Text:### Estimating the Area under a Curve #### (a) Estimate the Area Using Right Endpoints To estimate the area under the graph of \( f(x) = \frac{4}{x} \) from \( x = 1 \) to \( x = 5 \) using four approximating rectangles and right endpoints: \[ R_4 = \] #### (b) Repeat the Estimation Using Left Endpoints To estimate the area under the same graph using left endpoints: \[ L_4 = \] #### (c) Determine the Accuracy of Each Estimate By looking at a sketch of the graph and the rectangles, determine for each estimate whether it is an overestimate, underestimate, or the exact area. **Underestimate** \[ 1. \quad L_4 \] **Exact** \[ 2. \quad R_4 \]
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