A difficult differential problem to solve.

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i have been assigned a series of Q from my physics class and i find this Q hard to solve. give me a clue how to approach. help would be better appreciated.

show for short time y= yo -(t+(e^-bt)-1)(g/b^2) reduces to * y=y0 -1/2 gt^2

* find velocity and acceleration as a function of time.
 
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Approximate the function by its second degree MacLaurin polynomial.
 
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