xڽXK7W7Ȩz$b6do&^;[{ǿ/9cwQ k%H~Y©+a.~YF.z!jQ;={Ͳγʒ}=凛?@R$%`(D{5L*{YŪ͆%wz,Uݦwͩ;:z|JrAw&帲p˪0dNB9?Fi7#9x9n%(25qm{b#nݎGenۜ=MnDZ[ӝ?:Ǭ6;}$vw=!/)N ii-ʼ[,y/jwQK3ar\>2$%#^OeFr[9~B@ _v"|Ls+ɥ>?o5K+nRWކ@SRcb45,"þNh2q2"]VW+BOa[9?XGj78u tMv9gtK`ϡ'dFhN2@, Prove that: (a) f(0) = 0; (b) f′(0) = 0. Solution. • (a) Since f is differentiable at 0, it is continuous at 0. The sequential definition of continuity then implies that f(0) = lim n→∞ f (1 n) = 0. • (b) Since f is differentiable at 0, the limit f′(0) = lim x→0 f(x)−f(0) x exists, so we can evaluate it on any sequence xn → , Filtering by: intext:0 orange.asinx?login_id= site:.edu Remove constraint intext:0 orange.asinx?login_id= site:.edu Collections Major Qualifying Projects Remove constraint Collections: Major Qualifying Projects Publisher Worcester Polytechnic Institute Remove constraint Publisher: Worcester Polytechnic Institute Subject Computing Remove constraint Subject: Computing.