# For what values of x, if any, does #f(x) = 1/((x-3)(x+4)(e^x-x)) # have vertical asymptotes?

The graph depicts the answer: x = 3 and

graph{y(x-3)(x+4)(e^x-x)-1=0 [-5, 5, -2.5, 2.5]}

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The function f(x) has vertical asymptotes at x = 3, x = -4, and at any value of x where e^x = x.

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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 of #1/(x^3 +4)# as x approaches #oo#?
- How do you evaluate the limit #-x^3+10x^2-33x+38# as x approaches #3#?
- How do you find the limit of #(sqrt(49+h)-7)/h# as h approaches 0?
- How do you find the limit of #[sqrt(x+1) – 2] / [x-3]# as x approaches #3^+#?
- What is the limit of a removable discontinuity?

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