What is the slope of #x^2y^2=9# at #(-1, 3)#?
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To find the slope of the curve (x^2y^2 = 9) at the point ((-1, 3)), we first need to express the equation in terms of (y). Taking the derivative implicitly with respect to (x), we get:
[2x y^2 + 2x^2 y \frac{dy}{dx} = 0]
Then, solving for (\frac{dy}{dx}), we have:
[\frac{dy}{dx} = -\frac{x y^2}{x^2 y} = -\frac{y}{x}]
Now, at the point ((-1, 3)), the slope is:
[\frac{dy}{dx}\bigg|_{(-1, 3)} = -\frac{3}{-1} = 3]
So, the slope of the curve (x^2y^2 = 9) at ((-1, 3)) is (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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