Section 8.2 L’Hospital’s Rule

Section 8.2 L’Hospital’s Rule Learning Targets: I can evaluate limits with indeterminate form 0/0 I can evaluate limits with other indeterminate forms.

L’Hospital’s Rule Suppose that f(a) = g(a) = 0, that f and g are differentiable on an open interval I containing a, and that g’(x) is not equal to 0 on I if x is not equal to a. Then NOTE: This is NOT the quotient rule!!

Example 1 Find

Example 2 Find

Example 3 Find

L’Hospital’s Rule can also be applied to one-sided limits! Example 4 Find

Indeterminate forms involving infinity Example 5 Find SIMPLIFY! SIMPLIFY!

SKIP! c) Find (Hint: Find both sides) d) Find We need a common denominator to subtract fractions!

8.2A Homework #5, 7, 9, 11, 33, 37, 41, 49, 62, 64 - 66

Other Indeterminate Forms Limits that lead to indeterminate forms, __________, ___________, and ____________ can be handled by taking logarithms first. Typically, taking a logarithm will lead to another indeterminate form where we can use L’Hospital’s Rule.

Example 6 Find We still can’t do L’Hop because we don’t have a QUOTIENT. REMEMBER: This is our answer for the natural log of our function…

Example 7 Determine whether exists and find its value if it does. We still can’t do L’Hop because we don’t have a QUOTIENT. REMEMBER: This is our answer for the natural log of our function…

Example 8 Find

8.2B Homework Complete the worksheet on pages 8-9 in your packet. and #5, 11, 33, 49; Due Monday 