For what values of x, if any, does #f(x) = 1/((x-2)(x+2)(e^x-1)) # have vertical asymptotes?
Vertical asymptotes occur whenever the denominator of a rational function equals zero. In this case, one of the three binomials in the denominator must equal zero.
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The function f(x) = 1/((x-2)(x+2)(e^x-1)) has vertical asymptotes at x = 2 and x = -2.
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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.
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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- What is the limit of #sin^4(x)/x^0.5# as x goes to infinity?
- What is the limit of #(2x^2+3)^(1/2) - (2x^2-5)^(1/2)# as x approaches infinity?
- What is the limit of #sinx / x# as x goes to infinity?

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