MATH 19A Midterm: MATH19 Harvard Midterm1F04sol19 Fall 04

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15 Feb 2019
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\bu have two hours to take this midtcrm. Anv ansrver in dccirnal forrn nrust bc accuratc to threc decirnal places. urtless otherwise specificd. Pace l. ourself by keeping track r-if horv rnany problerns vou have lefl to go trnd horv much tirne renrairrs. You do not have to arrswer the probierns in anv particular order. so rnovc to another problenr if rorr fincl you are stuck or spending too nurch tirne ou a sitrgle problcrn. )"or1 u"ill rreecl to jrrstifl" voul ans\vers carefulll. unsujrstarrtiated ansrvers rvill receive 1itt1e cir no creclit (except if the ciirections for that questiou specificalll"sa\r no justificatiort is rrr"cessarl". sucir as a trrre/false section). Please be sure to rvlitc uetrtll illegible ans\vcrs rvill rcceive little cir no credit. If rnore space is ueecled. rrse the back of thc plcvious pagc to continue your rvork. Be srrre to urakc- a note of this on tire ploblerri pilge so tlrat tlie graclel ktiolvs rlltere to firrcl \"orlr ans\,"ers.