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mthsc206-fall-2010-notes-15.2-limits

# mthsc206-fall-2010-notes-15.2-limits - 3 If you can’t...

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Limit Guidelines for functions of two or more variables When computing limits of two or more variables, try the following steps. Step 1: Try direct substitution. Step 2: If direct substitution yields an indeterminate, look for algebra techniques to allow cancellation of a factor that is causing the indeterminate form. (Factor polynomials, multiply by 1 in the form of the conjugate, combine fractions, etc.) Never write a limit is equal to 0 0 . Step 3: If algebra fails, do any of the limit theorems, such as the Squeeze Theorem, apply? Step 4: If steps 1-3 fail, try taking a limit along a couple of paths. However: 1. Be sure your path passes through the limit location. 2. If you find two valid paths that yield di ff erent limits, then the limit will not exist.
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Unformatted text preview: 3. If you can’t ±nd 2 paths that give di²erent limits, YOU CAN’T MAKE ANY CONCLUSIONS!! PATHS CAN ONLY SHOW A LIMIT DOES NOT EXIST. YOU CANNOT USE PATHS TO PROVE A LIMIT EXISTS. 4. You can only use the Squeeze Theorem to show a limit exists. DO NOT SAY A LIMIT DOES NOT EXIST BY THE SQUEEZE THEOREM. SUCH A STATEMENT WILL RESULT IN THE LOSS OF ALL POINTS FOR THE PROBLEM. Also, be very careful to use correct limit notation. All of your limit problems should have some type of limit notation used in the solution. You are being graded on your use of this notation. Whenever you take a limit along a path, be sure to state what the path is and then use notation appropriate to the path. 1...
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