How do you find the vertical asymptotes of f(x) = tan(πx)?
The vertical asymptotes occur whenever
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graph{(y-tan(pix))=0 [-10, 10, -5, 5]}
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To find the vertical asymptotes of the function f(x) = tan(πx), we need to determine the values of x for which the function approaches infinity or negative infinity.
The vertical asymptotes occur when the tangent function has undefined values, which happen when the angle is equal to (2n + 1)π/2, where n is an integer.
In this case, we have πx = (2n + 1)π/2. Solving for x, we get x = (2n + 1)/2.
Therefore, the vertical asymptotes of f(x) = tan(πx) occur at x = (2n + 1)/2, where n is an integer.
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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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