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

See below.

So in general, vertical asymptotes occur when the denominator in the function is zero, such that it's value doesn't exist,

Therefore, we need

As it turns out, this is really quite hard to solve. I would use a graphical calculator or app to solve this.

But if we want to find solutions analytically then we could use the Taylor expansion for

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The function f(x) = 1/(e^x-3x) 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.

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