Local Linearization - Calculus - Solved Exam, Exams of Calculus

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MATH 105 Exam 2 Review November 10, 2004 1. Find dy/dz for each of the following. e, In2, arctan 2 ave consta ats } (a) y= a? +27 +e? +e? +In2+In (22) + arctan2 # dua n2-2% 2% sb -2 *[2x + n2-2" +e + Z| (b) y = V@- arctan (52) Preto Rule Zt 7 nts = | SER + Cectent x > dk: re = t< "a rcta (sx) arr + (c) y = In(tan(2e""))) Coo(K? dy | » tnd | (-sin()) 2x] BRO SP) em a +e™ . 3 3 3 fovte! Sin Ww moars (Sino). (@) y=sin (ain) m ft G ay lo. x eee “coef X18 Ted eacesme) ~ 4) ee ) ze? S Sin (a parcsintx Ind tars tn Ox Cin 4 #avesin x)* ev, lnd ave constants kK _——. Qushient ule —-} 2. Consider the curve defined by «° + y? = sry (known as the Folium of Descartes). (a) Find = ov DifLeventiation. 2x + By" : oy + $x fy ( Prod. Rule) a z q ay cd 2 : -tuys sx wa 2) = 2 Ax J dy 9, - aAf4y- By? dy es 34° St (Gx f) (b) Find the equation of the tangent line (the local linearization) at the point te 4, Wwhet's }? ms ee Sl Z 7 = ilk - 4 : L Se a -'% S ; siltb =>b + 3 Se, OF x +b => 4? = ex + £ 3. Use local linearization (tangent line approximation) to estimate V66. £0) = x" f() & £(A)+ F(A) (xe) £'(e) = ig. The = 6 Ff % (x-64) - 2 _/6& Choe acted kane | ox 6 +E G&-O)= 8% - BS we leno Je.