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Step 1: Decide if you are going to run a left-hand limit right-hand limit, or overall limit.
This example is specifically asking for a right-hand limit. |
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Step 2: Try Option 1: Plug it in Always try plugging in the you are heading towards. In this example we get division by zero, which means Option 1 has failed. |
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Step 3: Try Option 2: Factor and Cancel No factoring or canceling is possible in this example. |
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Step 4: Back to Option 1: Plug It In with an that is really, really, really close to the that you actually care about. You will need to use that to approximate the value on the top of your fraction and the bottom of your fraction.
In this example we need a number to the right of that is really, really, really close to the . In this example I am going to use . Remember the actual doesn’t really matter because you aren’t really doing this on a piece of paper, it is all a conceptual process in your head.
The top of the fraction would be considered a since 1 is a large number compared to a decimal.
The bottom of the fraction would be considered a . Since your that you use will always be larger than the 2, the result will always be a positive decimal. |
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Step 5: Use logic to evaluate the final result from Step 4.
Here we have a divided by a, which means the number is getting huge, and since we have . So, . |
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Final Result:
Meaning: The right-hand limit as approaches of is . There is a vertical asymptote at . Remember you only need a one-sided limit to equal for there to be a vertical asymptote.
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