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The diagram below shows upper and lower sums for the function f(x)=√√x+1 using 4 subintervals. Use upper and lower sums to approximate the area of the region using the 4 subintervals. Round to three decimal places.

The diagram below shows upper and lower sums for the function f(x)=√√x+1 using 4 subintervals. Use upper and lower sums to approximate the area of the region using the 4 subintervals. Round to three decimal places.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The image displays a mathematical problem illustrating upper and lower sums for the function \( f(x) = \sqrt{x + 1} \) using 4 subintervals. The objective is to approximate the area of the region using these subintervals, and to round the answer to three decimal places. ### Diagram Explanation The graph on the right shows the curve of the function \( f(x) = \sqrt{x + 1} \) along with vertical rectangles representing the upper and lower sums. The region under the curve from \( x = 0 \) to \( x = 2 \) is approximated by these rectangles. - **Upper Sum:** The rectangles are drawn such that their top side touches the curve at the left endpoint. - **Lower Sum:** The rectangles are drawn such that their top side is below the curve, beginning at the right endpoint of each subinterval. ### Instructions Select the correct pair of upper and lower sums from the options provided: - Option a: Lower: 3.036; Upper: 3.536 - Option b: Lower: 1.518; Upper: 1.768 - Option c: Lower: 6.072; Upper: 7.072 - Option d: Lower: 1.268; Upper: 2.018 The correct option is highlighted with an arrow pointing to option a, indicating that the correct values for the lower sum and upper sum, rounded to three decimal places, are 3.036 and 3.536, respectively. The problem emphasizes understanding of integration approximation through Riemann sums, specifically using upper and lower sums.
Transcribed Image Text:The image displays a mathematical problem illustrating upper and lower sums for the function \( f(x) = \sqrt{x + 1} \) using 4 subintervals. The objective is to approximate the area of the region using these subintervals, and to round the answer to three decimal places. ### Diagram Explanation The graph on the right shows the curve of the function \( f(x) = \sqrt{x + 1} \) along with vertical rectangles representing the upper and lower sums. The region under the curve from \( x = 0 \) to \( x = 2 \) is approximated by these rectangles. - **Upper Sum:** The rectangles are drawn such that their top side touches the curve at the left endpoint. - **Lower Sum:** The rectangles are drawn such that their top side is below the curve, beginning at the right endpoint of each subinterval. ### Instructions Select the correct pair of upper and lower sums from the options provided: - Option a: Lower: 3.036; Upper: 3.536 - Option b: Lower: 1.518; Upper: 1.768 - Option c: Lower: 6.072; Upper: 7.072 - Option d: Lower: 1.268; Upper: 2.018 The correct option is highlighted with an arrow pointing to option a, indicating that the correct values for the lower sum and upper sum, rounded to three decimal places, are 3.036 and 3.536, respectively. The problem emphasizes understanding of integration approximation through Riemann sums, specifically using upper and lower sums.
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Step 1: given information

given function

 f left parenthesis x right parenthesis equals square root of x plus 1 space a n d space n equals 4 space space l i m i t space o f space i n t e g r a t i o n space i s space 0 space t o space 1.

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