Find the degree $n$ taylor polynomial $p_{n}(x)$ for $f(x) = exp(x)$ about a point a = 1. find the smallest positive integer $n$ such that the remainder formula for the taylor approximation guarantees that (the absolute value of) the remainder is less than $10^{-3}$ for all $0\leq x \leq1$.

Arefrigeration system at your company uses temperature sensors fixed to read celsius (°c) values, but the system operators in your control room understand only the fahrenheit scale. you have been asked to make a fahrenheit (°f) label for the high temperature alarm, which is set to ring whenever the system temperature rises above –10°c. what fahrenheit value should you write on the label?