111 {E ptsﬂ‘l'e aregiventhe following informaﬁonaboutthofmction f : E.

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{I} We will construct am ﬂiﬂﬂﬂ linear function, L,

an approximation of I" on the interval [[1, E]. nm=L “I {a} Dnﬂiointerval [l]. 111 Lisalinoaragmoximation ofthefunolion r at out}.

FinrlanIto-coronationforl_.:Jr‘_|1 [151's 1.

Ltn- . “tore ﬂ 5 Jr 5 1. [ll-1. .uI‘IHEIInthointerval[1.2]1 Lisalinear illictionanditsmapnisaline moseslopeisf'm.

Find mommionforux], 15x52. Mote, Liscontinuousatx-t] Lu]. .wnoreisxsl [inwmrrloweﬂiink that the imotion I. might boa-good approxirnaljon

oftlroflliction fontho interim [1. 2]? [1:1 Dnﬂiointenral [2.3]1 Lis a linear fmction and itsgraph isaline whom-slope iof' [2}.

Find ariexproosion foer, 2 s x: 3. LlIi- .whereﬂsxsl