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Math 155, Lecture Notes Bonds Name Section 8.7 Indeterminate Forms and Capitals Rule Back in the Chapter 1 we applied algebraic methods for dealing with the following limits: 2x 2 2 3x 2 1 and LIM

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How to fill out section 87 indeterminate forms

01

Start by identifying if the limit is in the form 0/0 or ∞/∞.

02

If it is in the form 0/0, factor out the common terms and simplify the expression.

03

Apply the L'Hopital's Rule by differentiating the numerator and the denominator separately.

04

Take the limit of the differentiated expression as x approaches the given value.

05

If the limit still remains indeterminable, repeat the process until a determinable limit is obtained.

06

If the limit is in the form ∞/∞, rationalize the expression by multiplying the numerator and denominator by the conjugate of the highest-power term.

07

Simplify the expression and try to factor out common terms.

08

Apply the L'Hopital's Rule if necessary and take the limit as x approaches the given value.

09

Continue to repeat the process until a determinable limit is obtained.

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