Consider the error in using the approximation sin(x) - x on the interval [-1, 1]. (a) Reasoning informally, on what interval is this approximation an overestimate? An underestimate? (For each, give...

Extracted text: Consider the error in using the approximation sin(x) - x on the interval [-1, 1]. (a) Reasoning informally, on what interval is this approximation an overestimate? An underestimate? (For each, give your answer as an interval or list of intervals, e.g., to specify the intervals -0.25 < x="">< 0.5="" and="" 0.75="">< x="">< 1,="" enter="" [-0.25,="" 0.75),="" (0.75,1]="" enter="" none="" if="" there="" are="" no="" such="" intervals.)="" (b)="" use="" the="" error="" bound="" for="" taylor="" polynomials="" to="" find="" a="" good="" smallest="" bound="" for="" the="" error="" in="" approximating="" sin(x)="" with="" x="" on="" this="" interval:="" error="" bound="Now," consider="" the="" error="" in="" using="" the="" approximation="" sin(x)="" x="" x="" +="" +="" on="" the="" same="" interval.="" (c)="" reasoning="" informally,="" on="" what="" interval="" is="" this="" approximation="" an="" overestimate?="" an="" underestimate?="" (for="" each,="" give="" your="" answer="" as="" an="" interval="" or="" list="" of="" intervals,="" e.g.,="" to="" specify="" the="" intervals="" –0.25="">< x="">< 0.5="" and="" 0.75="">< x="">< 1,="" enter="" [-0.25,="" 0.75),="" (0.75,1]="" enter="" none="" if="" there="" are="" no="" such="" intervals.)="" (d)="" use="" the="" error="" bound="" for="" taylor="" polynomials="" to="" find="" a="" good="" smallest="" bound="" for="" the="" error="" in="" approximating="" sin(x)="" with="" x="" +="" +="" on="" this="" interval:="" error="" bound="">