# How do you find the instantaneous slope of #y=1/x# at x=4?

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To find the instantaneous slope of ( y = \frac{1}{x} ) at ( x = 4 ), you need to calculate the derivative of the function at that point. Using the power rule for differentiation, the derivative of ( \frac{1}{x} ) is ( -\frac{1}{x^2} ). Substituting ( x = 4 ) into the derivative, you get ( -\frac{1}{4^2} = -\frac{1}{16} ). Therefore, the instantaneous slope of ( y = \frac{1}{x} ) at ( x = 4 ) is ( -\frac{1}{16} ).

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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.

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