|
|
| Line 1: |
Line 1: |
| − | <span class="exam">Consider the region bounded by the following two functions: | + | <span class="exam">Divide the interval <math>[-1,1]</math> into four subintervals of equal length <math>\frac{1}{2}</math> and compute the left-endpoint Riemann sum of <math>y=1-x^2.</math> |
| − | ::::::::<span class="exam"> <math style="vertical-align: -5px">y=2(-x^2+9)</math> and <math style="vertical-align: -4px">y=0</math>.
| |
| − | | |
| − | <span class="exam">a) Using the lower sum with three rectangles having equal width, approximate the area.
| |
| − | | |
| − | <span class="exam">b) Using the upper sum with three rectangles having equal width, approximate the area. | |
| − | | |
| − | <span class="exam">c) Find the actual area of the region. | |
| | | | |
| | {| class="mw-collapsible mw-collapsed" style = "text-align:left;" | | {| class="mw-collapsible mw-collapsed" style = "text-align:left;" |
Revision as of 09:46, 18 February 2017
Divide the interval ![{\displaystyle [-1,1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/51e3b7f14a6f70e614728c583409a0b9a8b9de01)
into four subintervals of equal length Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}}
and compute the left-endpoint Riemann sum of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=1-x^2.}
Solution:
(a)
(b)
(c)
| Final Answer:
|
| (a)
|
| (b)
|
| (c)
|
Return to Sample Exam