L’Hopital’s Rule
What are Indeterminate Forms?
Applying L’Hopital’s Rule:
• Check that the limit of f(x) / g(x) is an indeterminate form 0 / 0 .
• Differentiate f and g separately.
• Find the limit of f’(x) / g’(x).
Indeterminate Form of Type 0 / 0Suppose that f and g are differentiable functions on an open interval containing x = a, except possibly at x = a, and that
How about some examples?Find the following limits:
1.
2.
3.
4.
Indeterminate Form of TypeSuppose that f and g are differentiable functions on an open interval containing x = a, except possibly at x = a, and that
How about some examples?Find the following limits:
1.
2.
3.
Indeterminate Form of TypeCan sometimes be evaluated by rewriting the product as a ratio:
1.
2.
Indeterminate Form of TypeCan sometimes be evaluated by combining the terms and manipulating the result to produce quotient
1.
2.
Indeterminate Form of TypeCan sometimes be evaluated by first introducing a dependent variable
And then computing the limit of lny. Since
The limit of lny will be an indeterminate form of type
How about an example?Show that
Let’s practice