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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