How to find the asymptotes of #f(x) = (x+3)(x2)^3 # ?
There are no asymptotes for this one.
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To find the asymptotes of the function ( f(x) = (x + 3)(x  2)^3 ), we need to consider vertical asymptotes and horizontal asymptotes separately.
Vertical asymptotes occur where the function approaches infinity or negative infinity as ( x ) approaches a certain value. They typically arise from the denominator of a rational function being equal to zero.
Horizontal asymptotes occur when ( x ) approaches positive or negative infinity, and the function approaches a constant value.

Vertical Asymptotes: Set the factors of the function that can make the denominator zero equal to zero and solve for ( x ). In this case, we only have one factor that can make the function undefined, which is ( x  2 = 0 ). Solving for ( x ), we get ( x = 2 ). Therefore, there is a vertical asymptote at ( x = 2 ).

Horizontal Asymptotes: To find horizontal asymptotes, analyze the behavior of the function as ( x ) approaches positive or negative infinity. Since the highest power of ( x ) in the function is ( x^3 ), and there are no terms in the function that can offset its effect, the function will behave like ( x^3 ) for large values of ( x ). Therefore, there is no horizontal asymptote because as ( x ) approaches infinity, ( f(x) ) will also approach infinity.
In summary, the asymptotes of ( f(x) = (x + 3)(x  2)^3 ) are:
 Vertical asymptote at ( x = 2 )
 No horizontal asymptote.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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