1. Clicker Question 1 What is lim x->  ln(x) /  x ? – A. 0 – B.  – C. 1 – D. -  – E. 2

2. Clicker Question 2 What is lim x->  x 100 / e x ? – A. 100 – B. 100! – C.  – D. 1 – E. 0

3. Application: Arc Length (2/28/14) What is the length of a given arc? More specifically, given the function f (x), how long is the curve of f as x goes from a to b? Call this length s. Well, look at little short lengths  s. By the Pythagorean Theorem,  s   ((  x) 2 + (  y) 2 ) Factoring out  x and going to the limit we get

4. An Example of Arc Length Find the arc length of f (x) = x 2 as x runs from 0 to 2. The answer must be more than the straight line distance from (0,0) to (2,4), which is 2  5, or about 4.472. Well, which is a tough one! So, use numerical integration: Simpson with n=2 gives (1 + 4(  2) + 2(  5) + 4(  10) +  17) / 6  4.650

5. Exact Answer? Can we find the exact arc length of x 2 from (0, 0) to (2, 4)? This involves a trig sub followed by a clever use of integration by parts. If you’re feeling adventurous, try it! This (sort of) is an example in the text.

6. Assignment for Monday Read Section 8.1 (omit, if you wish, pages 541-2). Do Exercises 1, 2, 3, 7, and 13. (On #3, evaluate the arc length integral by Simpson’s rule with n=2 (i.e., 5 data points), accurate to 3 decimal places.)