MAT 119 PAST EXAMS (2010-2017), Exams of Calculus

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Muhiddin UGUZ METU Department of Mathematics Calculus with Analytic Geometry First Midterm Exam | ede : Been 119 Last Name : | cad. Year : < : | Semester : Fall Name : a No = Coord. : Firat Arikan Dept. : Sec. No D 18.11.2017 Signature at : LD. ee : 9.30 6 Questions on 4 Pages | Duration : 120 minutes Total 100 Points ar iz yas. «jase «as SOLUTIONS SHOW YOUR WORK ! 4 vl4+ing Q.1 (4 x 5 = 20 pts) Consider the function y = f(x) = ei an ( ard ). In och fey fe) to be defined , vu need to bave (a) Find the domain of f. | x70, f4&x BO ond 50 xo — For oy ed fle) is ae WS. Goce | | dom(): | f ,+00) | (b) Find f’(z). | | rege gE) Carcha( liter )) orcten (J t4ax ) \ “ f QT 4eax te (l¢dax) pref, CET Pee?) , , . 24dnx alittx Xx | (c) Show that the function is invertible on its domain. Fer x>+ — eock of portent ox ) 4 ee? —-,- Uta 2 May positive and hence ft)’ 0. Also f 65 cight-eont, ad xed. Thus, ee/ on b>) H fallows p | af f i One-to-one cad Nerec Invertible da ity domain d (d) Let f-1(«) be the inverse function. Find its derivative af at x= ot/4, LZ | } as ond f(i)= e% We howe (