How do you find the vertical asymptotes of f(x) = tan(πx)?

Answer 1

The vertical asymptotes occur whenever #x=k+1/2,kinZZ#.

The vertical asymptotes of the tangent function and the values of #x# for which it is undefined.
We know that #tan(theta)# is undefined whenever #theta=(k+1/2)pi,kinZZ#.
Therefore, #tan(pix)# is undefined whenever #pix=(k+1/2)pi,kinZZ#, or #x=k+1/2,kinZZ#.
Thus, the vertical asymptotes are #x=k+1/2,kinZZ#.

You can see more clearly in this graph:

graph{(y-tan(pix))=0 [-10, 10, -5, 5]}

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Answer 2

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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Answer from HIX Tutor

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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