How do you find vertical asymptotes using limits?
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To find vertical asymptotes using limits, follow these steps:
- Determine the rational function's expression.
- Set the denominator equal to zero and solve for the variable(s).
- The values obtained in step 2 are potential vertical asymptotes.
- Take the limit of the function as it approaches each potential asymptote from both sides.
- If the limit approaches positive or negative infinity, then there is a vertical asymptote at that value.
- Repeat steps 4 and 5 for each potential asymptote to confirm their presence.
Note: It is important to consider any restrictions on the domain of the function, as these may affect the existence of vertical asymptotes.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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