高等数学B(2)学习通超星期末考试答案章节答案2024年

高等数学B(2)学习通超星期末考试章节答案2024年/ananas/latex/p/888173

答案:127324/ananas/latex/p/567043

答案:80/ananas/latex/p/3638592

答案:是收敛于,其他情形发散/star3/origin/1fa18d87b1daecc14f3138b8508089b4.png

答案:，为任意常数/star3/origin/1800f3cb70fe88d76a56a1d689bd710c.png

答案:，为任意常数/star3/origin/8de65c7f404d189f768aed9a3c97e0ba.png

答案:，为任意常数/star3/origin/921780e944c00f97b049ac9db2e0cdf6.png

答案:，为任意常数/star3/origin/abea63eb374ce21627c6b76344d3b2f1.png

答案:二阶/star3/origin/09f381b056a130ce04bac9e6b20caada.png

答案:9/star3/origin/36cdfc8d94bcaa337ce262e96e1a2295.png

答案:，为任意常数/star3/origin/668484ea4e737861db30017af3e5426d.png

答案:，为任意常数/star3/origin/1a90cf745871fb445aff4e6895f84a22.png

答案:，为任意常数/star3/origin/dd3f1d497ada73def9421392201bdce5.png

答案:，为任意常数/star3/origin/6bee7fe43533ba1c1fc41a68e4956f51.png

答案:，为任意常数/star3/origin/830e44d75b0adfcece809e888d7ed846.png

答案:，为任意常数/star3/origin/e1f21ce4f42760617f906dde01abfefb.png

答案:2/star3/origin/4a5355001e35ba8fe8096b8fb72a40fe.png

答案:;(-48,45,-36/star3/origin/18d3785159322ae50d5f79e071f6406d.png

答案:5/star3/origin/7861f2767363775a8b3a9d176e7b9c17.png

答案:2/star3/origin/1a4b73d77f33986d5b528bc4c166743b.png

答案:III/star3/origin/2b5656090f888ffb4e64684de44f5fbd.png

答案:III/star3/origin/59003098a0435c1b1a5e19a5e19a2b6d.png

答案:V/star3/origin/4e58de44864e1b069ebffb29d7eae5b0.png

答案:2/star3/origin/41b62a782498e72630b179f7e503955f.png

答案:2/star3/origin/2e108a5ad7f072aaeb5989ededac12f4.png

答案:4/star3/origin/6c44a665100037091998e93e722c8166.png

答案:40/star3/origin/3a4f1f4abc1020b81e603ffcaecff202.png

答案:30/star3/origin/cacf9b48748607ff75b67f5ec9c3f044.png

答案:4/star3/origin/30a83d71b2b006a86ff4c78362f1bf6a.png

答案:1/star3/origin/d40151a0289397466e7377ca22d0c598.png

答案:5/star3/origin/6de908a95a4c8bc3cc756a595b7ba775.png

答案:18/star3/origin/2a934140ceac231b827bbe30bcbde735.png

答案:3/star3/origin/905c6a8ed620a7a5cef382404bdc6cba.png

答案:2/star3/origin/531c85686376f048aa8a28ebaf82c660.png

答案:y^2+z^2=3x;z^2+y^2=3x;3x=y^2+z^2;3x=z^2+y^2;y^2+z^2-3x=0;/star3/origin/5e7fcfffeaa17882dfadb361079a9f35.png

答案:4x^2-9(y^2+z^2;4(x^2+z^2/star3/origin/c548ef6025640ec308a0f0223634b210.png

答案:椭圆/star3/origin/bc2b96321d82fba93455f14768f984c4.png

答案:双曲抛物面/star3/origin/63d5fc7748de7b7475562806b64ea5f4.png

答案:轴/star3/origin/89809d0268079f44beea4834790e4c4e.png

答案:轴/star3/origin/e719a98494b663b95737ed879e892552.png

答案:轴/star3/origin/9c0063ce14b5ce3165d78660366cb86b.png

答案:半径为1的圆/star3/origin/e2a724e264c4dfb38e9d24ca021671de.png

答案:半径为1的一个圆/star3/origin/2ea0778de5e070855845e9bfa33e9cde.png

答案:1/star3/origin/abd8a4890ba02731e3cd9a6c7f8db3bc.png

答案:6/star3/origin/e5b8be71d6269be829679707c3d3e7b6.png

答案:45/star3/origin/d660f43b484051e9e7b5a81f1fb25d9c.png

答案:(1,1,1/star3/origin/9943ce80691e74b4f64cf6f3ee13e454.png

答案:x-2y+3z-9=0/star3/origin/863779422c4e1ecc8c966f0e35ecd8e2.png

答案:x-y+2z-9=0/star3/origin/8b11f14de53f359c21c053c8622eedfc.png

答案:相交/star3/origin/b6f9d87c675f08086ff14b54110d73b4.png

答案:与平行,与垂直/star3/origin/a9204526a7e01480b188162e75f5afaf.png

答案:(-3,3,-2/star3/origin/1c40bf71fab4a9c67d27182fb3c2460c.png

答案:30/star3/origin/ab7fa35ff477d2d398a2db6f37776ba0.png

答案:60/star3/origin/f56e18d359c5841dc9fae87d3bb082d8.png

答案:60/star3/origin/9d1c68188914890f29195aa4b24b7e78.png

答案:平行/star3/origin/15fcc84431d91496c95951436e1b610f.png

答案:垂直于/star3/origin/dcca6b211e363ffc4b972f8ce29a6906.png

答案:(11,13,-3)/star3/origin/2405797170fda88b5843617779fdd7e8.png

答案:-1/2/star3/origin/32cdde4b649e93b592b6571c154ad388.png

答案:-2/star3/origin/66be4a2abdd2525ebb8b78fcebcbb1dc.png

答案:{(x,y,z/star3/origin/11c3b41574e4b45ed91305cd946bd349.png

答案:{(x,y/star3/origin/ed8c5d6ff3f2de6801790bb8c98894c8.png

答案:{(x,y/star3/origin/2dfed74c7ddb9f78ddda25d476ff7730.png

答案:不存在/star3/origin/5a3d12ecc9b942b572087f384ae5ea80.png

答案:;/star3/origin/26e5a93d9b78f76cf15e56a522605b7b.png

答案:（1）（2）/star3/origin/a892f98f951d90062d5f8c5f5ef72ca7.png

答案:x/(x^2+y^2;y/(x^2+y^2;(y^2-x^2/star3/origin/714ecfdf76f08b39015d00e144685352.png

答案:2/star3/origin/3ed54ba37b2252927a12c28e120189f5.png

答案:;4dx+dz/star3/origin/541972ff053bd17490fbd663fa522088.png

答案:;6dx+6dy+4dz/star3/origin/a4df9d18901c39880c9cd6ca85dd8820.png

答案:-0.0101;-0.01/star3/origin/f1ba0710895f0ac56a050a14536eb9ab.png

答案:2/star3/origin/65312e1904965a8435e0aeb3cdff57b9.png

答案:连续,偏导数不存在;/star3/origin/e23cb98e82a9856780bbf1307f8125ea.png

答案:1、设

,

。2、设，

。3、方程组两边对x求导得

解得/star3/origin/da30fdff3f71726c033c04f6a76fe94b.png

答案:-x/y;-xy^(-1/star3/origin/65978aca81147f220b0f1c4563a317d9.png

答案:-1/star3/origin/ebcb6d5e1581bd240ea1596ca12ddcb0.png

答案:1、,

,,切向量:,切点,法平面方程:,切线方程:.2、令

,则

,点处的切平面方程为,即

,法线方程为.3、设

,则

.已知切平面的法向量为

.因为已知平面与所求切平面平行,所以,即,

,代入椭球面方程得,解得,则,

.所以切点坐标为.所求切平面方程为,即

.4、已知平面的法线向量为

.因为

,所以参数对应的点处的切向量为

.又因为切线与已知平面平行,所以,即,解得

,

.于是所求点的坐标为和./star3/origin/8ceba4bcce6a62c999758d00068bfac3.png

答案:;(-4,-2,1/star3/origin/13a2f190db55d8d37dd92ababb5da804.png

答案:;(1,-2,1/star3/origin/1b949abcb8fc12caf67440a713b43da7.png

答案:2x+y-4=0;2x+y=4/star3/origin/18a9801133e0a9c414c691168d31f85b.png

答案:;(x-2/star3/origin/ea1e36ae3ca23dfdd03b35a879094c5e.png

答案:定义域,,联立方程组,求得驻点为;

;

,

在点处,

,且,所以点是极大值点,极大值点为;

在点处,

,所以点不是极值点。设在上,到的距离为,则,

记,令解得:.所以

设球面方程为

,

是它的各面平行于坐标面的内接长方体在第一卦限内的一个顶点,则此长方体的长宽高分别为

,体积为

.

令

.

答案方程组

,即,得唯一驻点.

由题意可知这种长方体必有最大体积,所以当长方体的长、宽、高都为时其体积最大./star3/origin/f1267260c5b4bf603c9297e683d61743.png

答案:0/star3/origin/0c3c8060af62389141d9da9a5e898e67.png

答案:1/star3/origin/867ec643aa393a795e4a2c99138c8f2d.png

答案:1、.2、.3、.4、./star3/origin/4d63bcac4c408d6667a6a38d6f228b31.png

答案:1;y/2;y/star3/origin/b18f82378ca1e58166971152097c417f.png

答案:4;x/2/star3/origin/f8a8161870901642895e7de086f608ed.png

答案:0;y/star3/origin/ea9b85b26043bd99b4e3a24c4a8ca082.png

答案:1/2;0.5/star3/origin/077a847d6eaa79779c763ac109aac61d.png

答案:0/star3/origin/7d44408541141619a77ce305c156db64.png

答案:4/star3/origin/36ab8dc287f3ee0d8d29214df27c5f89.png

答案:(1).（2）.（3）.（4）./star3/origin/b05517cbf86e41ad28cace2d895dd08f.png

答案:1),则.2）,即,原式=.3)的参数方程为,,则./star3/origin/6a27139b92e109d799587e88fc724571.png

答案:2/star3/origin/d8b5edc9a2457c461a3685877f8606ab.png

答案:1/star3/origin/b1ab9c91aa7599369bf4c3e13fef3e6b.png

答案:1）,.2）.3）即,./star3/origin/163b22b62642ae858ddb331e86566136.png

答案:;-7/6/star3/origin/e577c98515fa26f84a5f47861a364965.png

答案:;1/35/star3/origin/a6107b02bd2654db941563018a92fbb3.png

答案:-18/star3/origin/2c116b45992ca5d98f6b02fb8087c2ec.png

答案:11/star3/origin/6f8ec487403db8e9abbbf72d9eb88190.png

答案:0/star3/origin/0381ed2a4253ad03fb87af489b2328f5.png

答案:1),.

.2)添加辅助线:,与L构成封闭曲线的正向,令,则,3）,即,此曲线积分与路径无关.原式=.4)因为在面内成立,

故为某函数的全微分../ananas/latex/p/5462001

答案:3/star3/origin/d237ded0b2a8f8a4b1201f709999fb4c.png

答案:0/star3/origin/9d0e5892c6800a58526651a335192396.png

答案:4/star3/origin/fa2b70a69c984858b077e7224030b7c6.png

答案:在C不含原点的闭区域的边界线时/star3/origin/05d79952443bcd78ae6b5639a0323cce.png

答案:L取逆时针方向,函数P、Q在闭域D上存在连续的一阶偏导数/star3/origin/f5fea90a2f446cc2ca7c9a64369949ef.png

答案:;1/star3/origin/71b8e28c537033fb3c0e6f63a0c5f6bc.png

答案:;1/2^n;1/(2^n/star3/origin/d311ba5f85780aea32abf04635066dce.png

答案:;n/(3n+1;;1/3/star3/origin/fb745d4e83c3b934ae974dfd2ce5ffa2.png

答案:;n/(n+1;;1/star3/origin/69b52ecbe9a33f02d7f0eea018b4f036.png

答案:可能收敛也可能发散/star3/origin/7e83eee6d31b596308f29898cbb4e24d.png

答案:未必收敛/star3/origin/745ac1787294450850671a6070d73678.png

答案:不一定收敛/star3/origin/e6787922a502c664cc9e35ee7ac9d8d7.png

答案:收敛/star3/origin/29e8b7ab8116fb81e80194b208823537.png

答案:收敛/star3/origin/66b11c4970246662e8475e0ab7641d91.png

答案:收敛/star3/origin/01a7ebb341ef13aa340be363b223eb4b.png

答案:发散/ananas/latex/p/3802353

答案:发散/star3/origin/0dbb11d13d93a785b4930db2c85042a1.png

答案:收敛/ananas/latex/p/5483340

答案:收敛/star3/origin/6420f9492504bd4d4651478b6e90c155.png

答案:收敛/star3/origin/3ad4d0cdb10822ef4164d8633f5ed2dc.png

答案:发散/star3/origin/b9aef3ee0ed862f0080ecc9fa186336e.png

答案:发散/star3/origin/86db6d5b84903de6f9fe3b031fc34ced.png

答案:收敛/star3/origin/3c75767abc9b64e408fc3a5aec221381.png

答案:收敛/star3/origin/4c606b72b6e86039b893d613a4522de3.png

答案:发散/star3/origin/994f688874b70cebab36e52899350b67.png

答案:收敛/star3/origin/2b2d6491e56ace2c107068743310f53c.png

答案:发散/star3/origin/98fcc976e57c763c142337c2ae879610.png

答案:收敛/star3/origin/2a834790ad0405fadc319909e6f5683b.png

答案:发散/star3/origin/50e381322b05907a3b78d9041f102921.png

答案:发散/star3/origin/d89045a49e25359beaff048b73b4845f.png

答案:发散/star3/origin/535ce31dd535c9dac718e8c4ea458a5f.png

答案:条件收敛/star3/origin/e234e13e5c8b07745df14a164b72d43b.png

答案:条件收敛/star3/origin/ab0535e0e9f700e6135d6ccdd3a01ff8.png

答案:绝对收敛/star3/origin/792743b91c3d03a44e5a97c73dc1e8e2.png

答案:发散/star3/origin/b071684858d677218eb376e74fe7d69f.png

答案:绝对收敛/star3/origin/6725c3be5702d7d57c46b6fe3ab1fd65.png

答案:发散/star3/origin/f807e8387d418de67020ff15736d5b01.png

答案:条件收敛/star3/origin/de0a608e4f4ee071c5c4128e8e5b6e76.png

答案:条件收敛/star3/origin/cf3879597dd8b225b3e0415298771df5.png

答案:绝对收敛/star3/origin/36ee7f426591374b579813a00bf500a3.png

答案:必要非充分/star3/origin/f8e4a8342f18c13bf73a8e2b7bf5e29f.png

答案:1）因为

,则

收敛半径为

从而该级数的收敛域为

.2）因为.根据比值审敛法:当

即

时,级数收敛;当

即

时,级数发散.当

或

时,级数也是收敛的.

该级数的收敛半径为

,收敛域为

.3）

4）/star3/origin/c6059ddf8dc770c2faa7a71be4f420a5.png

答案:;ln(1+x/star3/origin/ede85906b35298804aa4c475fa3db77c.png

答案:;[-2,4/star3/origin/d2d8f583c0de56b65bd202ebb504b825.png

答案:;3/star3/origin/f7d6fa07cf56cad5aa9b4556bec91a1c.png

答案:;1/star3/origin/d91f12293da915530fe33c36972dea18.png

答案:适合的一切都使级数绝对收敛平面x-3y-4z=12与三个坐标面围成的四面体的体积是____.（填数字）

答案:24/star3/origin/4edc603c132d7d47f8a04e8027b31625.png

答案:x^2+2y^2=16/star3/origin/30f58766d7e39d26a197cd627dfab150.png

答案:1/star3/origin/42976ee582925b55207d1e285cbb5626.png

答案:(3,4,-5)点(-3,2,4)在第(

)卦限:

答案:II/star3/origin/10a0d2309bc65656d78fddb25fc11d2a.png

答案:135/star3/origin/38a62b2c75de46d8d4fb72c767b51206.png

答案:1/5/star3/origin/0ce6ce2fe59c269962cb68b78fa57d93.png

答案:3x-y-3z+16=0/star3/origin/3c4c4457455ee7d2cdcb48da448d609a.png

答案:-1/star3/origin/b91675c4eb58635de8d479667fc38578.png

答案:y/1+e^z/star3/origin/f042d4d400de6b745db1c9ba9265ba0a.png

答案:30/star3/origin/3b49301941962c07f8c55d64b53ccbf8.png

答案:2/star3/origin/fcb884f4e84bf8aae2aae1e9bd14ebfd.png

答案:点非函数的极值/star3/origin/38b6d2350732c3563fa018a8ea3c31dd.png

答案:可导但不可微/star3/origin/afab82e1a4084503abe659c6027a3dc1.png

答案:不存在/star3/origin/2c0445eeb3bc2e653172a40ab8569ce2.png

答案:4/star3/origin/2840479aa3edba80653798df725a149c.png

答案:有极大值2/star3/origin/acb8b3d5c261c317be27f13b3cf7190e.png

答案:36/star3/origin/f618baecf6e9efe2bfe32f21ae3571d0.png

答案:PI/star3/origin/f8aeb46d8fd2322d8f11d032d3726c13.png

答案:PI/6;1/6PI/star3/origin/58b35ae0b18acb89846a7dd379570fc8.png

答案:sin1/2;1/2sin1/star3/origin/a795657e7d9b9d6d172e1563cd82a6db.png

答案:PI/8;1/8PI/star3/origin/917985751abc02026781b09f5f7dee17.png

答案:;6/55/star3/origin/bb3b862474ae2e6904506cadcd7f53be.png

答案:1-y/star3/origin/023543aee99cb48cdbf5f9f81710e582.png

答案:2/star3/origin/14cbd4bd9b1738c9ce27c3f13ef0cb08.png

答案:小于零根据二重积分的几何意义,下列不等式中正确的是()

答案::≤,≤/star3/origin/7a19021fd16100e8914f94652c483fa6.png

答案:椭圆/star3/origin/ab1831f711ae027ff7dc453f7396c0f4.png

答案:轴/star3/origin/1b7c56d3e3a31496d16e867a036294ab.png

答案:轴/star3/origin/0496d8b2b97a561e937fdcfe4c32a46b.png

答案:轴/star3/origin/ccc065f4999b3b84a659f65f3d29933f.png

答案:;x^5e^y/(1+x^6e^2y/star3/origin/49ff108357d1ada42edb614e620129e5.png

答案:;1/star3/origin/8cf8042d9f536c8eb25b64c6e74a72fa.png

答案:;e^x(1+x/star3/origin/ba2e267c96cba30f131dc189b9724303.png

答案:;sin2x^2+4x^2dos2x^2;4x^2dos2x^2+sin2x^2;-2pi/star3/origin/37f73f27040ed2e4c29647052e10e7d0.png

答案:;-sin(e^2ysin(x+2y/star3/origin/3ed120f5d90625043b7639ed6ddaf66d.png

答案:;e^xyln(x+y/star3/origin/0eaff0f93896823977307f1f42394af5.png

答案:;1+sin1;sin1+1/star3/origin/2a6a98f033d6db4200c0e23834d935e2.png

答案:-2xyf'/f^2；-2xyf'(x^2－y^2/star3/origin/0af3cf7bd227cc43b761261597c812b7.png

答案:;ye^xy+2x/(x^2+y^2/star3/origin/2ba0bd8f4e30bc2499187b1609fab677.png

答案:;e^t(cost-sint/star3/origin/02348b50f06df7087a72313831646443.png

答案:;x/y+2;2+x/y；4/star3/origin/5c66f291356cf361d61f19fea8c41d04.png

答案:1/star3/origin/f90b71aaf2374b34c20b93e080c75fcb.png

答案:yz/(e^z-1;xz/(e^z-1/star3/origin/dcee7f3fbe1ed868b39d155bbda99204.png

答案:yz/(z^2-xy;xz/(z^2-xy/star3/origin/f766c5576c392c49da2867ab0e89548e.png

答案:1/(e^z-1;1/(e^z-1/star3/origin/04b5706f0b88f88bccf43ebff3bedd5c.png

答案:(y-x;(y-x/star3/origin/48e4ddb030916a98cbc32a9126bb668e.png

答案:yz/(z^2-xy/star3/origin/a006a13ff329841c6a9bd45f5b5a059e.png

答案:z/(x+1;z^2/y(x+1/star3/origin/03e2b9854c64d18087fecf9ef658cb5d.png

答案:;0;;0/star3/origin/c98538b84316f69a52a938c7b7eea8c4.png

答案:-1;-1/star3/origin/33a043b3f31857f8d3a74549f7ff8c1e.png

答案:;1/3/star3/origin/31fa8835045ce4f82b0f3e014f0cb567.png

答案:1/star3/origin/055a135d40a716b997948589d33f304d.png

答案:;-1在平面xOy上求一点,使它到x=0,y=0及x+2y-16=0三直线距离平方之和为最小,这一点的横坐标=

，纵坐标=

.(分式用a/b表示,)

答案:8/5;16/5/star3/origin/4981c27fcf284919aa3cc5e3e1fc0459.png

答案:54;54;54/star3/origin/b17bb8c23a3d557e95d5d18644c4cdf4.png

答案:3a;3a;3a/star3/origin/f1d22da315c780bfc4a861e972e2476a.png

答案:3a;3b;3c/star3/origin/a26a59102a0f1d46156a60454292997b.png

答案:6912要造一个容积等于256各单位的长方体无盖水池,则水池的长=____,宽=____,高=____,时,则水池的表面积最小.

答案:8;8;4/star3/origin/cb7bde93dfa7526f1a3594d1549afc8a.png

答案:12;12/star3/origin/63abfce8482ed47bff3fde226cbb74dd.png

答案:1/star3/origin/7be48ea9f8c9e810391bf201410b5459.png

答案:-pi/star3/origin/7729f66f60a47e356998dc2c04caf7fe.png

答案:41pi/2;/star3/origin/51b415f6a622af935a771cc195f156a0.png

答案:pi/4/star3/origin/c4dfff01f3ac8dc79d0bd459131e24e0.png

答案:5pi/4/star3/origin/10a34e8e4d6dc2d1fafb33ed69fb826a.png

答案:10*2^1/2/9;10*2^(1/2/star3/origin/4b15a94ec32d35a93a9524cdc5651f1c.png

答案:18pi/star3/origin/5a97b6fad55e7a9307cffe5f2029b22c.png

答案:32pi/3/star3/origin/a8895ead64304b84ec32d6227cd57138.png

答案:;16pi/star3/origin/485434c5b57432325b1ae1a9a37cfd93.png

答案:;pi/48/star3/origin/7b4c59cd771a8ca6f6f6ec87c95f5d80.png

答案:;1/2^n;2^(-n/star3/origin/3cb25dfa67f854b6e21a802a3dcdfce1.png

答案:;1-sqrt(2/star3/origin/676c5e248e79f91f10e2558983ecda6f.png

答案:;;1/star3/origin/14978ed83fa36082658850ca5e675640.png

答案:;；2/3;/star3/origin/ece9a286f4120af65ec9de52e5e39187.png

答案:可能收敛也可能发散/star3/origin/62e8cd5943719c709b6c72f1035bbd07.png

答案:未必收敛/star3/origin/b8b7ff7f24eaaf2ae42534307951b2d6.png

答案:不一定收敛/star3/origin/8e959f6c