设函数[tex=1.857x1.286]G6WxJ307HB2e1l7Qz3uNbQ==[/tex]在闭区间[tex=1.929x1.286]vPlUmwL8t1REs9r1XOy2kg==[/tex]上连续,在开区间[tex=2.071x1.286]Q9EbYIIWqK0gqhJcCkS6lw==[/tex]内可导,且[tex=3.929x1.286]yF7pvVInh0eInoseQrSNooOIScDfazfDCPMtH7DfBOY=[/tex],若极限[tex=6.571x2.071]MqOfsQLAB/zeVSdv1WggGLqchS9Lj/X+AmLKN2Mtp6ZjfsC8Zqc0W11hwjAr0ZsNdoUpQrAzHLckJ+1vyLPCig==[/tex]存在,证明:(1)在[tex=2.071x1.286]Q9EbYIIWqK0gqhJcCkS6lw==[/tex]内[tex=3.714x1.286]FOh2uNZfgGlH8S+OVIqrUA==[/tex];(2)在[tex=2.071x1.286]Q9EbYIIWqK0gqhJcCkS6lw==[/tex]内存在点[tex=0.5x1.286]cFLrzlMvECfU5CTqcvierw==[/tex],使[tex=7.714x2.714]gzM60KSvwplMcF58TO8u2dU/V2piuch2E1X2EWAq8T2tMW5aaDddAeP67XGZSLEjVkGIdLS/IgjJpctXT7GHGPzy+8N8PMGD0wwm/e2gq/M=[/tex];(3)在[tex=2.071x1.286]Q9EbYIIWqK0gqhJcCkS6lw==[/tex]内存在与(2)中[tex=0.5x1.286]cFLrzlMvECfU5CTqcvierw==[/tex]相异的点[tex=0.571x1.286]IvGNOcnlsPar7nw7Fd55Kg==[/tex],使[tex=7.214x1.286]gsb/5UaDnUD8XdPUF2TBamf03bdSvuobfcNAeIoG7EUwAqBBb1XK2sOUHMnHmMB0[/tex][tex=7.071x2.5]wOzTTci5ZM5vNI7JuR3k3ApIJCKN2nOrNe2VyFImWPej6nOblfzwRVRZEsKlr/pniR6jHkdk/9kZHHsPyc87eQ==[/tex]。
举一反三
- set1 = {x for x in range(10)} print(set1) 以上代码的运行结果为? A: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} B: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10} C: {1, 2, 3, 4, 5, 6, 7, 8, 9} D: {1, 2, 3, 4, 5, 6, 7, 8, 9,10}
- 设 [tex=1.857x1.286]G6WxJ307HB2e1l7Qz3uNbQ==[/tex] 在 [tex=1.929x1.286]vPlUmwL8t1REs9r1XOy2kg==[/tex] 上连续,在 [tex=2.071x1.286]Q9EbYIIWqK0gqhJcCkS6lw==[/tex] 内可导。证明在[tex=2.071x1.286]Q9EbYIIWqK0gqhJcCkS6lw==[/tex] 内至少存在一点 [tex=0.5x1.286]cFLrzlMvECfU5CTqcvierw==[/tex],使得[tex=7.571x2.643]oMl9s9NJfa8eLuyTQI6HjH0P3SEFjEgVhry1X5YzHG2/urD013vNXJJQd3Z32mtf[/tex]。
- 设[tex=1.857x1.286]G6WxJ307HB2e1l7Qz3uNbQ==[/tex]在 [tex=1.929x1.286]vPlUmwL8t1REs9r1XOy2kg==[/tex]上连续,在 [tex=2.071x1.286]Q9EbYIIWqK0gqhJcCkS6lw==[/tex] 内可导, [tex=3.714x1.286]c/7qSEbCZzHa0GZbNzqjfQ==[/tex], [tex=10.0x2.857]8QU3aWoJhSGnV7gONGqJzSghLQ+KEInuY2K6MnVJ+Wk5YlEQiyB8Wqv7BbxuAXo5yCzk81I8VVIfToJCJ4GmxmMLMNdMXTfhFWk0s3tSAIQ=[/tex], 试证在[tex=2.071x1.286]Q9EbYIIWqK0gqhJcCkS6lw==[/tex]内至少存在一点[tex=0.5x1.286]cFLrzlMvECfU5CTqcvierw==[/tex], 使[tex=8.5x1.286]lzQv80ZLeUASAnm5Ehn9hVJg9V+x+lqkAVSWNeYnKEvlJrsAtdq3wpYAtQsMarU6[/tex]。
- 设 [tex=1.857x1.286]G6WxJ307HB2e1l7Qz3uNbQ==[/tex], [tex=1.786x1.286]jg4bgzd+cKocBmeYxC3pQQ==[/tex] 都在[tex=1.929x1.286]vPlUmwL8t1REs9r1XOy2kg==[/tex]上连续, 且在 [tex=2.071x1.286]Q9EbYIIWqK0gqhJcCkS6lw==[/tex]内可微, 又对于[tex=2.071x1.286]Q9EbYIIWqK0gqhJcCkS6lw==[/tex] 内的 [tex=0.571x1.286]XubEW9+1+hkJqH7jXe5MrA==[/tex] 有 [tex=3.857x1.286]qn2AJfbmoLEE7Tl4Pd7PllGjDjTXiWMPwR865hJoScY=[/tex],则在[tex=2.071x1.286]Q9EbYIIWqK0gqhJcCkS6lw==[/tex] 内至少存在一点[tex=0.5x1.286]cFLrzlMvECfU5CTqcvierw==[/tex],使[tex=7.929x2.714]ao6sL/whefGaAsRSHCRhNiVXgLPr34z9bPcIDVLf6DMRHjGMXhoN6zhrAaTH3O84i7BBeG6R6i5gyw2pKK7+y/bCILss0MsxhUnAVzRFssI=[/tex]
- 设函数[tex=1.857x1.286]G6WxJ307HB2e1l7Qz3uNbQ==[/tex]在闭区间[tex=1.929x1.286]0UMnlwcnmtQAgoeNciVtQA==[/tex]上连续,在开区间[tex=2.071x1.286]ObtC4nfyqFyi8RRxjLkdQA==[/tex]内可导,且[tex=3.929x1.286]rry4HS9j03SSzVB9RUT23Q==[/tex],若极限[tex=6.571x2.071]/N7iQJH5tJ1CHV4Wb82/t5l1SAe/HM45edYGn0PE4xrh0AdQiW8wb2OwnWB4aOnN[/tex]存在,证明:(I)在[tex=2.071x1.286]ObtC4nfyqFyi8RRxjLkdQA==[/tex]内[tex=3.714x1.286]FOh2uNZfgGlH8S+OVIqrUA==[/tex];(II)在[tex=2.071x1.286]ObtC4nfyqFyi8RRxjLkdQA==[/tex]内存在点 [tex=0.5x1.286]cFLrzlMvECfU5CTqcvierw==[/tex],使[tex=7.643x2.714]fcrG91uS2Lgsl5jlblCwp4sMxk/MN/6kuDXBJl4caC8ytdJsZobTJ8c0T5gsNKc3EJfimDaPvtxGWRFRLvHt3w==[/tex];(III)在[tex=2.071x1.286]ObtC4nfyqFyi8RRxjLkdQA==[/tex]内存在与(II)中 [tex=0.5x1.286]cFLrzlMvECfU5CTqcvierw==[/tex] 相异的点[tex=0.571x1.286]IvGNOcnlsPar7nw7Fd55Kg==[/tex],使[tex=14.214x2.5]3nYslbo2LIrp8HSf5Pgt38MgVldrREnqVEVagfdSawttEikm+75KWA1ISMYL3EGRS5n2H2XtMBUp+nj+ic9Fzw==[/tex]。(本题满分10分)