<prompt> Pata kikomo lim _n mshale wa kulia inftykushotoint_01 ex2 n d xkulian.  <response>: Rekebisha varepsilon0 ya kiholela. Kwa kuwa chaguo la kukokotoa yet ni laini, kwa t in0, varepsilon grafu yake iko juu ya tangent y1t lakini chini ya sekunde y1a_ varepsilon t, ambapo a_varepsilonfrac1varepsilonleftevarepsilon-1right. Kwa hivyo kwa frac1n leq varepsilon inashikilia leftint_01 ex2 n d xkulian geqkushotoint_01kushoto1fracx2nkulia d xkuliankushoto1 frac13 nkulian mshale wa kulia e1 3, maandishi as n mshale wa kulia infty, na leftint_0 1 ex2 n d xkulian leqkushotoint_01kushoto1fraca_varepsilon x 2nkulia d xkuliankushoto1fraca_varepsilon3 nkulian mshale wa kulia e a_varepsilon 3, text as n rightarrow infty Tangu a_varepsilonfrac1varepsilonleftevarepsilon-1 kulia mshale wa kulia 1, kama varepsilon mshale wa kulia 0, tunapata lim _n mshale wa kulia inftyleftint_01 ex2 n d xkuliane1 3. Jibu: e1 3 