设[tex=6.071x1.357]4LgfSyTm0h7bq9xqSv7G4LNyI9eXQ7t6nf458Xe37zjS4V81lBtGaGjd6xQTx6KK[/tex]在[tex=1.857x1.357]bawv/j+LZ1l+o4ciN/29dA==[/tex]上连续，在[tex=2.214x1.357]mpyYBdP7k8056w1o+qOOxw==[/tex]内可导，证明：存在[tex=3.286x1.357]EV4pc+LBkNBOhd4NZUA5NQ==[/tex]，使得[tex=16.357x3.357]Uyz5s0rmQIddjb5Jc2T/YRSnI70CPiP9kSoxG/LsBEQsOFwZaIYio/xDEuz4rvImZ3GEM+gn+IQRe1Rq9HOufnlmnLgQiRTLLWlyd2m5PpNiisTat4EvIByMSXzh8HVQPts8b6b0urtNgk9oqPzz4TXb9tDW2RcYR0g9UvBgcN8wfdw1empP7P1zbq+Jg68Psxp+i3UzfEuBVHPM7mUbhwNryRi3jXo3t34CuHeOXN8=[/tex]

设f(x),g(x)在[a,b]上连续，f'(x),g'(x)在(a,b)内存在，证明：[tex=17.786x3.357]Uyz5s0rmQIddjb5Jc2T/YRSnI70CPiP9kSoxG/LsBEQsOFwZaIYio/xDEuz4rvImZ3GEM+gn+IQRe1Rq9HOufvnQiCWpcE11pvqN0xZJm/9KE+3ILJyinkbz30kkqN83nBVLYkFVQ5Q6bXnW5mivpRYmOIa68RyGaPOOBgZpbqIs0vbZIm+NG7i5KeSOpSw25GXWnjDh4XFSb/YU/DTLhRFsqEAar70PWY11q/CwycKXYOjkDRYRk8aKw6BcLHjIh1xbd4EKeQm+5a6T3/Mwrr+JtOiMIE4uj0wKS8tAEqo=[/tex]其中[tex=0.5x1.214]qqpHxP43oSTaBTohjVBA4g==[/tex]在a和b之间。