一联轴器，由分别分布在半径为R₁和R₂圆周上的8只直径相同的螺栓耗联接(如图所示)。则内圈(R₁)螺栓横截面上的切应力τ₁与外圈(R₂)螺栓横截面上的切应力τ₂的比值为( )。<img src='https://img2.soutiyun.com/ask/5763001-5766000/48207949b48a9e9bedcb87827bdcc2e3.jpg' />

<img src='https://img2.soutiyun.com/ask/uploadfile/5097001-5100000/f2bbe390993478cb409f9ccc28c1b771.png' /> A．<img src='https://img2.soutiyun.com/ask/uploadfile/5097001-5100000/d3b0b10d995224fcb7aa65edfd06358c.png' />B．m₂gh C．<img src='https://img2.soutiyun.com/ask/uploadfile/5097001-5100000/8ac00e32bd2362d9b994ce31e73becdb.png' />D．0

A．<img src='https://img2.soutiyun.com/latex/latex.action' /> B．<img src='https://img2.soutiyun.com/latex/latex.action' /> C．<img src='https://img2.soutiyun.com/latex/latex.action' /> D．<img src='https://img2.soutiyun.com/latex/latex.action' />

设幂级数<img src='https://img2.soutiyun.com/ask/2020-12-14/976788824298225.png' />的收敛半径为R,而<img src='https://img2.soutiyun.com/ask/2020-12-14/976788837697991.png' />的收敛半径为R,若把幂级数<img src='https://img2.soutiyun.com/ask/2020-12-14/976788854253938.png' />的收敛半径记为R,证明: (1)<img src='https://img2.soutiyun.com/ask/2020-12-14/976788868991781.png' />; (2)当R₁≠R₂时,<img src='https://img2.soutiyun.com/ask/2020-12-14/976788887921864.png' />.

如题图14-13所示，曲率半径为R₁和R₂的两个平凸透镜对靠在一起，中间形成一个空气薄层，用波长为λ的单色平行光垂直照射此空气层，测得反射光中第k级的暗环直径为D。 (1)说明此暗环的空气层厚度e应满足<img src='https://img2.soutiyun.com/ask/2020-10-10/971196776104917.jpg' />。 (2)已知R₁=24.1m，λ=589nm，k=20，D=2.48cm，求R₂。 <img src='https://img2.soutiyun.com/ask/2020-10-10/97119600531383.jpg' />

因柱形电容器内、外导体截面半径分别为R₁和R₂(R₁＜R₂),中间充满介电常数为ε的电介质.当两极板间的电压随时间的变化<img src='https://img2.soutiyun.com/ask/2020-12-29/978082344279563.png' />时(k为常数)，求介质内距圆柱轴线为r处的位移电流密度.

<img src='https://img2.soutiyun.com/ask/2020-11-19/974672657164018.png' />

一质点在平面上作曲线运动，t₁时刻的位置矢量为r₁=(-2i+6j),t₂时刻的位置矢量为r₂=(2i+4j).求:(1)在Δt=t₂-t₁时间内位移的矢量式;(2)该段时间内位移的大小和方向;(3)在坐标图上画出r₁、r₂及Δr. (题中r以m计,t以s计.)

两齿条以速度v₁和v₂做同向直线平动，两齿条间夹一半径为 r的齿轮(如图所示)。求齿轮的角速度及其中心O的速度。 <img src='https://img2.soutiyun.com/ask/2021-03-18/98493230474086.png' />

利用命题“若<img src='https://img2.soutiyun.com/ask/2021-01-20/979980914313406.png' />的收敛半径为R₁，<img src='https://img2.soutiyun.com/ask/2021-01-20/979980936623682.png' />的收敛半径为R₂，并且R₁≠R₂，则<img src='https://img2.soutiyun.com/ask/2021-01-20/979980968483504.png' />的收敛半径为R=min{R₁，R₂}，并且当|x|＜R时， <img src='https://img2.soutiyun.com/ask/2021-01-20/979981120012171.png' /> 求下列级数的收敛半径、收敛区间和收敛域： <img src='https://img2.soutiyun.com/ask/2021-01-20/979981142352448.png' />

<img src='https://img2.soutiyun.com/ask/2021-02-09/981733139186214.png' />

<img src='https://img2.soutiyun.com/ask/2021-01-21/980085788241153.jpg' />

<img src='https://img2.soutiyun.com/ask/2020-09-22/969639761479142.png' />

<img src='https://img2.soutiyun.com/ask/2020-09-01/967829909897877.png' />

(1)滑轮在3s内的转数。 (2)当t=3s时重物B的速度和经过的路程。 (3)当1=0时滑轮边缘上点C的加速度。 <img src='https://img2.soutiyun.com/ask/2020-12-09/976392049413852.png' />

匀质圆柱半径为<img src='https://img2.soutiyun.com/ask/2020-09-21/969553822137206.png' />、高为L,下底保持温度u₁,上底保持温度u₂.侧面温度分布为f(z) =<img src='https://img2.soutiyun.com/ask/2020-09-21/969553846224584.png' />.求解柱体内各点的稳恒温度.

人造地球卫星近地点离地心r₁=2R，(R为地球半径)，远地点，离地心r₂=4R。求： (1)卫星在近地点及远地点处的速率<img src='https://img2.soutiyun.com/ask/2021-02-08/981629164677512.png' />和<img src='https://img2.soutiyun.com/ask/2021-02-08/981629173633024.png' />(用地球半径R以及地球表面附近的重力加速度g来表示); (2)卫星运行轨道在近地点处的轨迹的曲率半径ρ。

<img src='https://img2.soutiyun.com/ask/2021-02-21/982799735258245.png' />

若幂级数<img src='https://img2.soutiyun.com/ask/2020-08-10/965908113007065.png' />的收敛半径分别是R₁和R₂，则R₁和R₂的大小关系是()。

流速场为<img src='https://img2.soutiyun.com/ask/2020-09-25/969883847382666.jpg' />求半径为r₁和r₂的两根流线之间流量的表达式.

<img src='https://img2.soutiyun.com/ask/2021-02-09/981718618897701.png' />

<img src='https://img2.soutiyun.com/ask/2021-03-19/984997623933356.png' />