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Chain Rule : Assume that we have two functions f(x) & g(x) and they both are differentiable. 1. If we define F ( x ) = ( f o g ) ( x ) then the derivative of F(x) is,
Graph f ( x ) = e x and g ( x ) = e - x . Solution There actually isn't a lot to this problem other than ensuring that both of these exponentials are graphed somewhere.
A 20-foot light post shows a shadow 25 feet long. At the similar time, a building nearby casts a shadow 50 feet long. determine the height of building? a. 40 ft b. 62.5 ft
lnx(1+x)
Example of Partial Fraction Decomposition Evaluate the following integral. ∫ (3x+11 / x 2 -x-6) (dx) Solution: The 1 st step is to factor the denominator so far as
If the points (5, 4) and (x, y) are equidistant from the point (4, 5), prove that x 2 + y 2 - 8x - 10y +39 = 0. Ans : AP = PB AP 2 = PB 2 (5 - 4) 2 + (4 - 5) 2 = (x
you are driving on a freeway to a tour that is 500 kilometers from your home. after 30 minutes , you pass a freeway exit that you know is 50 kilometer from your home. assuming that
Estimating the Value of a Series One more application of series is not actually an application of infinite series. It's much more an application of partial sums. Actually, we
Exponential smoothing It is a weighted moving average technique, this is described by: New forecast = Old forecast + a (Latest Observation - Old forecast) Whereas a = Sm
Find the series solution of2x2y”+xy’+(x2-3)Y=0 about regular singular pointuestion..
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