求该函数在指定点处的泰勒级数，并求其收敛域：[tex=10.143x1.286]EaQAyrNm2kSI7svDAfi4w2FlqPXYsEbTbSbmE6NfZ5+eAnFeWymg0vbuzfhirpKg[/tex]
解：由 [tex=2.0x1.0]pCnw3JsRBb35dEjM0AXbDw==[/tex] 和 [tex=2.143x0.786]7sCqPKbP66hcrOPfxoYK+Q==[/tex] 的幂级数展开式可得[tex=21.214x6.929]qeiYnKXLEhyhuGRg8yLtr5FsDx1YdgerdoaBWB/p36HhMMO1ucgjduBNElLdWiC/CNVw9kpKwUif0OtHMhvc8WgBBV3LCbR2GHM2K9N9F8CjBd4X6MVOUhG0GgZbkslCHlqRi4kyxg9pDbLgg9aJbWToEhVmFo+e/8enzzYNHv2hk/KhpdgBwEEv5T48HkV05HwJcu1X74fpdrrjPDvaxD+GfUZz9h/UNcYOrJI2wp/wJwe9yJrkvXJ6i10K36/geHi1emcwSP65p94pqZb/Pv9UkUXQou4PK13OOtP3IPedBtH7XadILPcKcwm2dvce[/tex]于是[tex=26.0x9.786]qeiYnKXLEhyhuGRg8yLtr0tz18rwvDH4fjZn2Opf9fQ/k+HjHq4lAcYwWZJYkYPm+BFdk4gLpNEyPg25ONv+QC76AOFEaCTJ4UqDLI4YtnUclXtgD1FDpYeUQJGNFN7UiappeQV7EonMhaObXoJxNPWvjspJTWS3kZsBYLWU4r6933PDTNSpEjUs4dx+SLV2Xd5yuSiCtpSmQCueKVkAfonnLszIIYZSUirxekVFkKs3kx/tV/eWiN2OfCE8MsZuM14ql5sN2w/hjFGVUEoqs4IqZLIYR/v0ihQHDnBrhwU9aiMRcY+otAunT/a0u7OLzHfoxGQKGHo4FBXjGQms1xxTSmU1SGtPl7FlP/3oX4fzt1dCp+khMuZ3Rv+cBjdRKLg8qKed2YYzlOwMoNbNuw==[/tex]其中[tex=15.429x4.643]szej6QDKzwjMjdHvUO6EUWeTFK8mQuB5QvxJQibJ3uBJgcwZRxf3Up8u+bbhTokKB1XvG57fjfRTcydUZCFW0Nrc3jdte+OZSV7DrhNLvd+g5/8hC7fe2qRbQqGvmk1sHcW8G2Qx/CF+wVlQerTeU/3hfmlrikLOEFdfJdT6FlHm6oRIPMu20sT0Xubs9gvx4RhAKp/+hjrPVudiolprfA==[/tex]其收敛域为 [tex=5.071x1.357]WafKDm5071vVz9IYJgBhj5opH6LenpHmjOoqLPYsZkw=[/tex]
举一反三
- 求该函数在指定点处的泰勒级数，并求其收敛域：[tex=8.929x1.357]w1dPtCfyu7tr/XsWpwrcndEShOuRu0Nw9MIuVsBHglI=[/tex]
- 求下列函数在指定点处的泰勒级数，并求其收敛域：[tex=3.571x1.357]HiWwm+KbNwf7T504aONniA==[/tex]，[tex=2.214x1.214]uyBPWQUsom6ZNUpKSZdHnw==[/tex]
- 求该函数在指定点处的泰勒级数，并求其收敛域：[tex=7.0x1.357]vGJ50zKC8gdsci5oBcei/I5vRWiU8Sjr20jxs/J2Rag=[/tex]
- 下列函数在给定点处的多大范围内能展开成泰勒级数?并求每个函数给定点处的泰勒级数：[tex=4.143x1.357]yN91K2k8f05PzqVF5Djdrg==[/tex]，在[tex=1.571x1.0]jHpz3JXoIDFh65htTlorKA==[/tex]点。
- 下列函数在给定点处的多大范围内能展开成泰勒级数?并求每个函数给定点处的泰勒级数：[tex=10.071x1.286]i6TJpIGttHfG2rCQ6TqMqLzVjVEqc+TK+8HzDlQ1uGAgjUKje0UraX1YNIwm5yyP[/tex].
内容
- 0
下列函数在给定点处的多大范围内能展开成泰勒级数?并求每个函数给定点处的泰勒级数：[tex=4.929x1.5]oplTTWzYb+li8LQIrD2ZsFt+F6/ZW/uknPcsS2lU5Hs=[/tex]，在[tex=1.786x1.0]OK0mYXKV9THVWMjDsQSyrQ==[/tex]点.
- 1
将函数 [tex=9.571x1.286]LBQTtZLtpmUEQrFQ21Og0zYLlmJjp/ivP06YgMMeXpMeoYoBl1mJN2BxZQvb41cM[/tex] 在指定点处展开成泰勒级数,并指出其收敛半径.
- 2
将此函数展开成麦克劳林级数，并求其收敛域：[tex=3.571x1.357]8MBRPhvCF6qRxyofAhjSjQ==[/tex]
- 3
将此函数展开成麦克劳林级数，并求其收敛域：[tex=5.143x1.5]IJwuJNbSgcLpUSCQjZhLKPiNlWXzSMzC3VWK34f7ZtY=[/tex]
- 4
将此函数展开成麦克劳林级数，并求其收敛域：[tex=6.643x2.429]kadv9dC0YndoPCBWaM4DZ4D2MbNojIH47pt0ju5hd60=[/tex]