For what values of x, if any, does #f(x) = 1/((x+1)(x-6)) # have vertical asymptotes?
f(x) will have vertical asymptotes where the denominator equals to zero. That is, where the limit of f(x) will rise or drop without bound.
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The function f(x) = 1/((x+1)(x-6)) has vertical asymptotes at x = -1 and x = 6.
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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.
- How do you find the limit of #(3x^2+6x)/(x^2-4)# as x approaches 2?
- How do you find the limit of #2x+5# as #x->7^-#?
- How do you find the limit of #sin(2x-sin(5x))# as x approaches pi?
- How do you find the limit of #(ln (ln (x) ) ) / ( ln (x) ) # as x approaches #1#?
- How do you evaluate the limit #sin^3(2x)/sin^2(3x)# as x approaches #0#?

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