Let #f(x)= 1x^3# and #g(x)= 1/x#, how do you find each of the compositions?
To find the composition of (f) and (g), denoted as ((f \circ g)(x)), and the composition of (g) and (f), denoted as ((g \circ f)(x)), follow these steps:

Finding (f \circ g): ((f \circ g)(x) = f(g(x))) Substitute (g(x)) into (f(x)) to get: ((f \circ g)(x) = f(1/x)) Then, replace (x) in (f(x)) with (1/x): ((f \circ g)(x) = 1  (1/x)^3) Simplify the expression: ((f \circ g)(x) = 1  \frac{1}{x^3})

Finding (g \circ f): ((g \circ f)(x) = g(f(x))) Substitute (f(x)) into (g(x)) to get: ((g \circ f)(x) = g(1x^3)) Then, replace (x) in (g(x)) with (1x^3): ((g \circ f)(x) = \frac{1}{1x^3})
Therefore, the compositions are: ((f \circ g)(x) = 1  \frac{1}{x^3}) ((g \circ f)(x) = \frac{1}{1x^3})
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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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