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Laur
Pe: 2013-01-26T09:47:57+02:00 In: In:

Limite laterale

Buna Ziua.Nu prea am inteles lectia asta si am 2 probleme ce nu stiu sa le rezolv.In speranta ca voi fi ajutat!

1.Sa se verifice daca urmatoarele functii au limita in punctele specificate:

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2.Sa se determine constantele a,b apartin R, pentru care functiile f:R->R au limita in punctele date:

    \[\begin{array}{l} a)f(x) = \\ \{ {x^2} + ax,x \le 1\\ \{ ax + 1,x > 1\\ {x_0} = 1.\\ b)f(x) = \\ \{ \frac{{x + a}}{{x + 1}},x \le 0;\\ \{ \frac{{2x + 1}}{{x + 3}},x > 0;\\ {x_0} = 0. \end{array}\]

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1 raspuns

  1. sandy_sc
    maestru (V)

    pt ca fuctia sa aiba limit in punctul Xo=2 trebbuie ca limitele lateralle
    sa existe s sa fie egale

    a)x<2 x–>2 ls==lim f(x)=lim 2*x+1=2*2+1=5 liimita la staanga ls=5
    x>2 x–>2 ld=limf(x)=lim5x=5*2=10 limita dreapta 10 =/=5
    ls=/=ld funtia nuu aare limita in punctul respectiv

    b)lim \frac{sinx}{x}
    Vom calcula lim sinx/x

    Plcam de lla inegalittatea sinx< x<tgx
    luam pima parte a inegalitatii si impartim prin x. oBTINEM
    SINX/X<1
    (1) LIM(SIN(X))<1

    RELUAM INEGALITATEA

    X<tg X => COSX<SIN X/X DARCOS X =1 PT X=0g
    ASARDAR 1>SINX/X (2)
    dIN (1) SI (2) => LIM SINX/X=1

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