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单选题 若函数f(x)的二阶导数连续,且满足f²(x)-f(x)=x,则
( )
B. 
D. 
学科：微积分(I)
时间：2025-09-17 13:00:10
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题目1单选题
设某产品的总产量的变化率为f(t)=10t-t2,那么t从t0=4到t1=8这段时间内的总产量为( )A. 136B. <img src="https://tihai-oss-cloud.itihey.com/img/648266701a10fdab1a19f9396bbe0713.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/b7da53ff73736120e569fad46b298db4.png">D. 68
题目2单选题
两椭圆曲线<img src="https://tihai-oss-cloud.itihey.com/img/a57b7ad31cf1313975596bd79365c5ed.png"> 及<img src="https://tihai-oss-cloud.itihey.com/img/c9e831dd486c3ad9b39ef52719e94c8e.png"> 之间所围的平面图形面积为( )A. pB. 2pC. 4pD. 6p
题目3单选题
曲线y=sinx,y=cosx,x=0以及<img src="https://tihai-oss-cloud.itihey.com/img/3b78041257834d8a271bf39d35353fb9.png"> 围成的图形面积为( )A. 0B. <img src="https://tihai-oss-cloud.itihey.com/img/c640524449475d79b82d4a0025cfbf8e.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/86ff24caecbed6dade8b9fb74036ed62.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/bf6ccc2ed1c10260bb166cd1b04e7a12.png">
题目4单选题
设f(x)连续,<img src="https://tihai-oss-cloud.itihey.com/img/d647d8bdcb690bd4ad2997a815f9bc4e.png"> ( )A. xf(x2)B. -xf(x2)C. 2xf(x2)D. -2xf(x2)
题目5单选题
<img src="https://tihai-oss-cloud.itihey.com/img/45319921572d35ce65d6e8a56028e6cf.png"> ( )A. <img src="https://tihai-oss-cloud.itihey.com/img/4591a90715f3074f7d1f9f2513fed0ad.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/3bdba72ab68662706f5365e73cbf4120.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/3f68b60b87bcf1962a1b066684c94997.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/41f33d40214e7e7d7febc8188c2ab7b1.png">
题目6单选题
一个食品公司正在增设网点,若经营费用增加率<img src="https://tihai-oss-cloud.itihey.com/img/76810028e464fa19c06b51b53a379788.png"> (百万元/年),而收入的增加率<img src="https://tihai-oss-cloud.itihey.com/img/1a9576f0669e34a8645cc25d05a07ddc.png"> (百万元/年),其中x表示增设的网点数,初期投入费用C0=100百万元,则欲使增设网点后利润最大,应增设( )家店.( )A. 32B. 36C. 40D. 44
题目7单选题
若函数f(x)的二阶导数连续,且满足f²(x)-f(x)=x,则<img src="https://tihai-oss-cloud.itihey.com/img/27167bdbc4bc7a1932488cb8cdaab5b5.png"> ( )A. f¢(p)-f¢(-p)B. <img src="https://tihai-oss-cloud.itihey.com/img/b242a45cfa5c1866addf57b2d8beb409.png">C. f(p)-f(-p)D. <img src="https://tihai-oss-cloud.itihey.com/img/0eb51049710518f0b1704306e66c39f5.png">
题目8单选题
曲线y=|lnx|与直线<img src="https://tihai-oss-cloud.itihey.com/img/d6b5b63f5215d6086dd6c61272764798.png"> ,x=e及y=0所围成的平面图形的面积A=( )A. <img src="https://tihai-oss-cloud.itihey.com/img/3ca1db3399243d62d699ea3fa25cd9fb.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/dc8af6f4b3ce7e5e98a085c6d9669ae4.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/06c21ae908e4c0f58179f453cae4ad6b.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/663ec4a60d78007a8a961c7eaf58ef30.png">
题目9单选题
设某企业边际成本是产量Q(单位)的函数<img src="https://tihai-oss-cloud.itihey.com/img/890111ea32b7d05274b97c19ce6d3603.png"> (万元/单位),其固定成本为C0=90(万元),则总成本函数为( )A. <img src="https://tihai-oss-cloud.itihey.com/img/27b4739afd278e682b735469fd984041.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/195da4a6a096abaec09702f0c3c1869d.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/e09286a0067f530f9fd8f1f9ab829a07.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/5f1a15867defb1e3859c4d3c31322fdf.png">
题目10单选题
将曲线y=x2与x轴和直线x=2所围成的平面图形绕y轴旋转所得的旋转体的体积可表示为Vy=( )A. <img src="https://tihai-oss-cloud.itihey.com/img/1ec24c622b25ebd28f943741333d7a7a.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/e5bce4176cadcb21b8178b35e810164f.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/b2cde4daf290509974646bcd387e770c.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/fc0e9d99ff532397eaa8735137044ac5.png">
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