Calculus Of One Real Variable – By Pheng Kim Ving
Chapter 8: Applications Of The Derivative Part 2 – Section 8.7: More Indeterminate Forms

8.7
More Indeterminate Forms

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1. The Indeterminate Quotient Forms

In Section 1.1.3 we discussed the indeterminate quotient form 0/0, and in Section 1.1.7 we handled the indeterminate

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2. The Indeterminate Sum And Difference Forms

which is just the difference form written in a different order. We gather them together here:

Example 2.1

Evaluate the following limit if it exists:

Solution

EOS

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3. The Indeterminate Product Forms

Consider these three trivial limits:

1.1.3 and 1.1.7,

are:

Example 3.1

Find the following limit if it exists:

Solution

EOS

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4. The Indeterminate Exponential Forms

Example 4.1

Evaluate the following limit if it exists.

Solution

= 1,

EOS

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Problems & Solutions

Solution

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Solution

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Solution

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Solution

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5. Prove this limit:

Note

Here x is fixed and h is variable.

Solution

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