# For what values of x, if any, does #f(x) = 1/((3x-2)sin(pi+(8pi)/x) # have vertical asymptotes?

All these asymptotes are displayed in the Socratic graph.

graph{y(y(3x-2)sin(3.1418(1+8/x))-1)(3x-2)(x+2)=0 [-3.1, 3.118, -1.446, 1.662]}

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The function f(x) has vertical asymptotes at x = 2/3 and x = 0.

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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.

- How do you find the limit as x approaches 1 of #sin(pix)/(x-1)#?
- What are the horizontal and vertical asymptotes on the graph of #f(x) = (x -1)/(x^2 + 2x + 1)#?
- How do you find the limit of #((2x^2-6)/(5x-x^2))# as x approaches infinity?
- How doI find limits in calculus?
- How do you find the limit of #(3(1-cosx))/x# as #x->0#?

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