# Calc05_1 - 5.1 Estimating with Finite Sums Greenfield...

• Notes
• 11

This preview shows pages 1–5. Sign up to view the full content.

5.1 Estimating with Finite Sums Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2002 Greenfield Village, Michigan

This preview has intentionally blurred sections. Sign up to view the full version.

time velocity After 4 seconds, the object has gone 12 feet. Consider an object moving at a constant rate of 3 ft/sec. Since rate . time = distance: If we draw a graph of the velocity, the distance that the object travels is equal to the area under the line. ft 3 4 sec 12 ft sec = 3 t d =
If the velocity is not constant, we might guess that the distance traveled is still equal to the area under the curve. (The units work out.) 2 1 1 8 V t = + Example: We could estimate the area under the curve by drawing rectangles touching at their left corners. This is called the Left-hand Rectangular Approximation Method (LRAM). 1 1 1 8 1 1 2 1 2 8 t v 1 0 1 1 1 8 2 1 1 2 3 1 2 8 Approximate area: 1 1 1 3 1 1 1 2 5 5.75 8 2 8 4 + + + = =

This preview has intentionally blurred sections. Sign up to view the full version.

We could also use a Right-hand Rectangular Approximation Method (RRAM).
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern