How do you find the vertical, horizontal or slant asymptotes for #f(x)= -1/(x+1)^2#?
No Slant Asymptote
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To find the vertical asymptote(s), set the denominator equal to zero and solve for ( x ). In this case, ( (x + 1)^2 = 0 ). Solving for ( x ), we get ( x = -1 ). Therefore, the vertical asymptote is ( x = -1 ).
To find the horizontal asymptote, examine the behavior of the function as ( x ) approaches positive or negative infinity. Since the degree of the denominator is greater than the degree of the numerator, the horizontal asymptote is at ( y = 0 ).
There are no slant asymptotes for this function since the degree of the numerator is less than the degree of the denominator.
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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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