# How do you find the instantaneous rate of change of g with respect to x at x=2 if #g(x)=2x^2#?

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To find the instantaneous rate of change of ( g ) with respect to ( x ) at ( x = 2 ) if ( g(x) = 2x^2 ), we find the derivative of ( g(x) ) with respect to ( x ), which represents the rate of change of ( g ) with respect to ( x ) at any given point.

The derivative of ( g(x) = 2x^2 ) with respect to ( x ) is ( g'(x) = 4x ).

Then, to find the instantaneous rate of change at ( x = 2 ), we substitute ( x = 2 ) into the derivative function:

[ g'(2) = 4(2) = 8 ]

So, the instantaneous rate of change of ( g ) with respect to ( x ) at ( x = 2 ) is ( 8 ).

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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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