MAT235Y1 Lecture 21: Mat235 note21

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16 Nov 2018
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144tauqeutplanesandlinearapproximations lkfcxl. tt fix rl exists at a then tlxl nirizat. im off at a flxkflaltflalcx. at (cid:5458) x a such that (cid:5458) (cid:2241) 0 tangent line at a fldtflallxalfht yuntl. 2(cid:1334) (cid:2026) fall is differentiable at lab if flxykflabltfabllxatfylabm bltl. ly(cid:2020) a thlxylly d ouxyl iineariz. ation off atcab suchthat (cid:1293) (cid:5441) o (cid:2782)slab. Writing (cid:39497) x aoyiy b. cz tix y flab we have a flab oxtfyla. doythoxtlzoy. If the partial derivatives fx. fi andarectsatcaibl thenfisdiffatca b existnearlab. Exi_iflx. de (cid:2930) (cid:2782) too since flx. co 0 wehave (cid:3598)1010 0 b0 similarly since flo (cid:2781)(cid:1323)0 (cid:1807)look 0. But f is not (cid:9398) at loo since it"s noteven cts at lo 0. Er showthat fix (cid:2781) xe is diff at clo. Find its linearization there and use it (cid:2241) appro. fm 005 (cid:2213) f txy yfy. Cts fun (cid:1323) neil f is diff everywhere. 1 linearration ux ykflloltfxcl. nl h tfy lo lq d. Ey an equationof a plane agentplanet ex at cl0.

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