# How do you find instantaneous velocity from a position vs. time graph?

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To find instantaneous velocity from a position vs. time graph, you need to find the slope of the tangent line at the point of interest on the graph. This tangent line represents the velocity at that specific instant. Mathematically, you can find the slope of the tangent line by calculating the derivative of the position function with respect to time at the given time instant. The derivative gives the velocity at that instant. Alternatively, you can calculate the average velocity over a very small time interval around the point of interest. As the time interval approaches zero, the average velocity approaches the instantaneous velocity.

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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.

- What is the equation of the line tangent to # f(x)=(x-3)^2-x^2-3# at # x=5#?
- What is the instantaneous rate of change of #f(x)=(x^2-3x)e^(x) # at #x=2 #?
- What is the equation of the line tangent to # f(x)=(3x-1)(x+4) # at # x=3 #?
- What is the equation of the normal line of #f(x)=sqrt(2x^2-x)# at #x=-1#?
- What is the equation of the line normal to #f(x)= x^3+4x^2 # at #x=1#?

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