Limits What does this mean?

Finding the area under a curve y=4x-x2 http://cs.jsu.edu/~leathrum/Mathlets/ riemann.html Text n 2 4 6 8 10 20 50 100 area

Find the area under the curve Use limits to determine the area... n 4 10 20 50 100 area

y=16-x2 between -3 and 4 Draw the curve and then use Left, Right and Mid bounds to determine the limit of the area.

y=4sin(x) Use limits to determine the area under one hill of the curve.

Limit and slope limslopenotes (pdf)

Determine the y-coordinate for each value of the domain below (8, ); (7, ); (6, ); (5, ); (4, ); (3, ); (2, ), (1.5, ); (1.3, ); (1.1, ) (1, )

Find 5 points on the graph that are increasingly closer to the point (1, 4) and use limits to determine the slope of the tangent at x=1.

Review 2. Find the area under y= - x2 - x+20 between x= -4 and x = 3. 1. Estimate the limit 2. Find the area under y= - x2 - x+20 between x= -4 and x = 3. n 2 5 10 20 50 100 area 35 37.5 38.1 38.16 38.19 38.195

limseqnotes

Limits to infinity (exponential functions)

Calculate the limit as x approaches infinity

Limits of sequences

Un lien utile pour les limites de séquences http://home.alltel.net/okrebs/page13 4.html

limseriesw/notes

Summation Notation

n’th partial sums Calculate the infinite sum by taking the limit of the n’th partial sum. State that the series is either convergent or divergent.

Sums to infinity

Find the sum

Express a repeating decimal as a fraction. 2.1353535…

4.2777…

2.7181818…

Use the infinite sum formula for geometric series to sum the following:

Interval of convergence

Limits of Functions

Type a/b, where a≠0

Type a/0, where a≠0

Type 0/0

expand and simplify

rationalize the denominator

Rationalize the numerator

Limits: Horizontal & Vertical Asymptotes

1. Limits from the Right and the Left

2. Limits from both sides

Next lesson: Continuity