# For what values of x, if any, does #f(x) = 1/(xe^x-3) # have vertical asymptotes?

There is a vertical asymptote at the solution to

So we know that there is a vertical asymptote, and we can describe where it occurs.

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The function f(x) = 1/(xe^x-3) has vertical asymptotes at x = 0 and x = ln(3).

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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 evaluate #( 5x^9-4x^2-2x+1)/(x^7-x^6+x-1)# as x approaches 1?
- Given #(sin x)^(3x^2)# how do you find the limit as x approaches 0?
- How do you find #lim_(x->5)(x^2+2)# using a graph?
- How do you find the limit of #1/(root3(x^2-4)# as x approaches #2^-#?
- How do you find the limit of #sqrt((4-x^2))# as x approaches #-2#?

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