What is the definition of instantaneous rate of change for a function?
Elijah AbramGiven that a function's instant rate of rate and derivative are the same, the definition is
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Isaiah AllenThe instantaneous rate of change of a function at a specific point is defined as the rate at which the function's value changes with respect to a small change in the independent variable, as that change approaches zero. Mathematically, it is the derivative of the function at that point.
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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.
- How do you find the average rate of change of #g ( x) =10x −3# over the interval [1,5]?
- What is the equation of the line tangent to #f(x)= sqrt(3-2x) # at #x=-2#?
- How do you find the equations of the tangent lines to the curve #y= (x-1)/(x+1)# that are parallel to the line #x-2y = 2#?
- How do you find the derivative of #3x^2-5x+2# using the limit definition?
- What is the equation of the tangent line of #f(x)=1/x-1/x^2+x^3# at #x=1#?
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