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 $0\leq x \leq1$.

Raj encoded a secret phrase using matrix multiplication. using a = 1, b = 2, c = 3, and so on, he multiplied the clear text code for each letter by the matrix to get a matrix that represents the encoded text. the matrix representing the encoded text is . what is the secret phrase? determine the location of spaces after you decode the text. yummy is the corn the tomato is red the corn is yummy red is the tomato