How do you implicitly differentiate #x^2 + y^2 = 1/2 #?
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To implicitly differentiate ( x^2 + y^2 = \frac{1}{2} ), differentiate each term with respect to ( x ), treating ( y ) as a function of ( x ) using the chain rule.
( \frac{d}{dx}(x^2) + \frac{d}{dx}(y^2) = \frac{d}{dx}(\frac{1}{2}) )
( 2x + 2y\frac{dy}{dx} = 0 )
( \frac{dy}{dx} = -\frac{x}{y} )
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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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