# What is the instantaneous rate of change of #f(x)=1/(x^2+2x+3 )# at #x=0 #?

This is merely f'(0)'s value.

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To find the instantaneous rate of change of ( f(x) = \frac{1}{x^2 + 2x + 3} ) at ( x = 0 ), you need to find the derivative of ( f(x) ) with respect to ( x ), and then evaluate it at ( x = 0 ). Therefore, the instantaneous rate of change of ( f(x) ) at ( x = 0 ) is given by ( f'(0) ).

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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.

- How do you find instantaneous rate of change for the equation # y=4x^3+2x-3#?
- How do you use the limit definition to find the slope of the tangent line to the graph #f(x)=9x-2 # at (3,25)?
- How do you use the limit definition to find the derivative of #y=x+4#?
- What is the equation of the normal line of #f(x)=x/(2-x^2)# at #x = 3#?
- How do you use the limit definition to find the slope of the tangent line to the graph #f(x) = sqrt(x+1)# at (8,3)?

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