How do you differentiate #(x^2 + x + 3 )/ sqrt(x-3)# using the quotient rule?
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To differentiate ((x^2 + x + 3)/\sqrt{x-3}) using the quotient rule:
- Identify (f(x) = x^2 + x + 3) and (g(x) = \sqrt{x-3}).
- Apply the quotient rule: ((f(x)g'(x) - g(x)f'(x))/[g(x)]^2).
- Find the derivatives: (f'(x) = 2x + 1) and (g'(x) = \frac{1}{2\sqrt{x-3}}).
- Plug the values into the quotient rule formula.
- Simplify the expression if necessary.
The differentiated expression will be:
[\frac{(2x+1)\sqrt{x-3} - (x^2 + x + 3)\frac{1}{2\sqrt{x-3}}}{(x-3)}]
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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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