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Interpretation of the second derivative : Now that we've discover some higher order derivatives we have to probably talk regarding an interpretation of the second derivative.
If the position of an object is specified by s(t) we know that the velocity is first derivative of the position.
v (t ) = s′ (t )
First derivative of any velocity is the acceleration of object; however since it is the first derivative of the position function we can also think of the acceleration as the second derivative of the position function.
a (t ) = v′ (t ) = s′′ (t )
Alternate Notation : There is couple of alternate notation for higher order derivatives. Recall as well that there was a fractional notation for the first derivative.
f ′ ( x ) = df /dx
We should extend this to higher order derivatives.
f ′′ ( x )= d 2 y / dx f ′′′ ( x ) = d 3 y/ dx etc.
Change of base: The final topic that we have to look at in this section is the change of base formula for logarithms. The change of base formula is,
Sketch the phase portrait for the given system. Solution : From the last illustration we know that the eigenvectors and eigenvalues for this system are, This tu
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a die was rooled 500 times and number of times 4 came up was noted if the imperical probability calculated from this information 7_10
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y=f(a^x) and f(sinx)=lnx find dy/dx? Solution) dy/dx exist only when 0 1 as the function y = f(a^x) itself does not exist.
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Derivative for Parametric Equations dx/dy = (dx/dt) / (dy/dt) , given dy/dt ≠ 0 Why would we wish to do this? Well, remind that in the arc length section of the Appl
1. Construct an isosceles triangle whose base is 7cm and altitude 4cm and then construct another similar triangle whose sides are 1/2 times the corresponding sides of the isosceles
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