Objective – L’Hopital’s Rule (Indeterminate Forms)

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Presentation transcript:

Objective – L’Hopital’s Rule (Indeterminate Forms) Lesson: Derivative Applications 2 Objective – L’Hopital’s Rule (Indeterminate Forms)

Find the limit:

Indeterminate Forms – Limits of the form 0/0 or L’Hopital’s Rule:

Applying L’Hopital’s Rule Check that the limit of f(x)/g(x) is an indeterminate form of 0/0 or . 2. Differentiate f and g separately 3. Find the limit of f’(x)/g’(x). If this limit is finite, + infinity, or – infinity then it is equal to the limit of f(x)/g(x).

EX 1: Find the limit using L’Hopital’s Rule.

Why does L’Hopital’s Rule Work? Basically, since , it is considered to be in indeterminate form. (Meaning other methods must be used to evaluate it). We will be using a tangent line approximation to approach the limit value.

If f and g are continuous & diff. at x = a, then: also so,

EX. 2: In each part, confirm that the limit is an indeterminate form and evaluate it using L’Hopital’s Rule

Ex. 3: Evaluate the limit Let’s try L’Hopital’s rule:

Therefore, L’Hopital’s rule doesn’t apply