1. AIM : How do we find limits of a function graphically & numerically? Do Now: Graph the piecewise function. HW2.2b – p76-7 # 3, 9, 22, 39, 40, 48 HW2.2b – p76-7 # 3, 9, 22, 39, 40, 48 Find the one-sided limits at x = -2 and 0.

2. Formal Definition of a Limit A limit only exists at a point if the left hand limit and the right hand limit exist and equal each other (converges at the same value). We can see this graphically (if the sides connect/are going the same direction) or algebraically (if the values of the one-sided limits are equivalent)

3. Finding Limits Numerically Find the limit of y = x 2 has x → 2 numerically by filling in the table below: XY = X 2 1 1.5 1.8 1.9 1.99 2-2- XY = X 2 3 2.5 2.2 2.1 2.01 2+2+

4. So why go through all that?

5. Practice 1.Find the limit as x → 0 + of f(x) = xlnx by filling in the table below: 2.Estimate the limit numerically or show that the limit does not exist: X10.50.10.050.010.0050.0001 f(x)

6. AP Practice – No Calculator If, then is a)ln9 b) ln27 c)3ln3 d)3 + ln3 e)non-existent