What is the slope of the tangent line of #x^3y^2-(x+y)/(x-y)^2= C #, where C is an arbitrary constant, at #(1,4)#?
Slope of tangent line is
graph{(x^3y^2-(x+y)/(x-y)^2-139/9)(203y-812+1303x-1303)=0 [-10.87, 9.13, -4.08, 5.92]}
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To find the slope of the tangent line at the point (1,4), you need to differentiate the given equation implicitly with respect to x, then substitute the values of x and y at the point (1,4), and solve for the derivative dy/dx. After that, evaluate dy/dx at the point (1,4) to get the slope of the tangent line. The result is the slope of the tangent line at the point (1,4).
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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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