Now use the limit definition to prove that limn→[infinity]an=1. That is, find the smallest value of M (in terms of t) such that |an−1|M. (Note that we are using t instead of ϵ in the definition in order to allow you to enter your answer more easily). M= 2/t-5 (Enter your answer as a function of t)

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)