For what values of x, if any, does #f(x) = 1/((x-5)(x+6)) # have vertical asymptotes?
William Abdallax = 5 , x = -6
Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation let the denominator equal zero.
solve: (x - 5 )(x + 6 ) = 0 → x = 5 x = -6 are the equations.
Here is the graph of the function. graph{1/((x-5)(x+6)) [-10, 10, -5, 5]}
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Axel AlvarezThe function f(x) = 1/((x-5)(x+6)) has vertical asymptotes at x = 5 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.
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