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若函数f(x)在[a,b]内具有二阶导数,且f(x<sub>1</sub>)=f(x<sub>2</sub>)=f(x<sub>3</sub>),其中a<x<sub>1</sub><x<sub>2</sub><x<sub>3</sub><b.证明:在(x<sub>¿762¿</sub>,x<sub>3</sub>)内至少有一点ξ,使得f"(ξ)=0.
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设f<sub>1</sub>(t),f<sub>2</sub>(t)均满足拉氏变换存在定理的条件(若它们的增长指数均为c<sub>0</sub>),且L[f<sub>1</sub>
设f<sub>1</sub>(t),f<sub>2</sub>(t)均满足拉氏变换存在定理的条件(若它们的增长指数均为c<sub>0</sub>),且L[f<sub>1</sub>(t)]=F<sub>1</sub>(s),L[f<sub>2</sub>(t)]=F<sub>2</sub>(s),则乘积f<sub>1</sub>(t)f<sub>2</sub>(t)的拉氏变换一定存在,且<img src='https://img2.soutiyun.com/ask/2020-12-16/976985160070298.jpg' />,其中β>0,Res>β+c<sub>0</sub>。
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设f(x)在[a,b]上连续,在(a,b)内连续可导,x<sub>0</sub>∈(a,b)是f(x)的唯一驻点。若f(x<sub>0</sub>)是极小值,证明:x∈(a,x<sub>0</sub>)时,f'(x)<0;x∈(x<sub>0</sub>,b)时,f'(x)>0。
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设函数f(z)在|z| 试证:M(r)在区间[0,R)上是一个上升函数,且若存在r<sub>1</sub>及r<sub>2</sub>(0≤r<sub>1</sub>
设函数f(z)在|z|
<img src='https://img2.soutiyun.com/ask/2020-08-06/965552417984214.png' />
试证:M(r)在区间[0,R)上是一个上升函数,且若存在r<sub>1</sub>及r<sub>2</sub>(0≤r<sub>1</sub>,r<sub>2</sub>≤R)使得M(r<sub>1</sub>)=M(r<sub>2</sub>),则f(z)=常数.
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如图所示正弦稳态电路,已知电源U<sub>S</sub>的频率为f时,电流表A和A<sub>1</sub>的读数分别为0和2A;若U<sub>S</sub>的频率变为f/2,而幅值不变,则电流表A的读数为( )。
A.0 B.1A C.3A D.4A
<img src='https://img2.soutiyun.com/ask/uploadfile/6492001-6495000/2b54182ffc03b3fd2dd65ff666d1dbc7.jpg' />
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若已知两个同频正弦电压的相量分别为=50∠30°V,=-100∠-150°V,其频率f=100Hz。求:(1)u<sub>1</sub>、u<sub>2⌘
若已知两个同频正弦电压的相量分别为<img src='https://img2.soutiyun.com/ask/2020-11-30/975591829782132.jpg' />=50∠30°V,<img src='https://img2.soutiyun.com/ask/2020-11-30/975591842005831.jpg' />=-100∠-150°V,其频率f=100Hz。求:(1)u<sub>1</sub>、u<sub>2</sub>的时域形式;(2)u<sub>1</sub>与u<sub>2</sub>的相位差。
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若f(x)在点x<sub>0</sub>具有直到n阶连续导数,并且那么当n为奇数时,f(x<sub>0</sub>)非极值:当n为偶数而f<sup>
若f(x)在点x<sub>0</sub>具有直到n阶连续导数,并且<img src='https://img2.soutiyun.com/ask/2021-01-22/980164129217826.png' />那么当n为奇数时,f(x<sub>0</sub>)非极值:当n为偶数而f<sup>(n)</sup>(x<sub>0</sub>)>0时,f(x<sub>0</sub>)为极小值:当n为偶数而f<sup>(n)</sup>(x<sub>0</sub>)<0时,f(x<sub>0</sub>)为极小大值.
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若f&39;<sub>x</sub>(x<sub>0</sub>,y<sub>0</sub>)=0,f&39;<sub>y</sub>(x<sub>0</sub>,y<sub>0</sub>)=0,则函数f(x,y)在(x<sub>0</sub>,y<sub>0</sub>)处( )。
A.连续
B.必有极限
C.可能有极限
D.全微分dz=0
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小球动能减小一半,速度从<img src='https://img2.soutiyun.com/shangxueba/ask/18801001-18804000/18803286/2016030115353541951.jpg' />F<sub>1</sub>、F<sub>2</sub>是力F的两个分力。若F=10N,则下列不可能是F的两个分力的是()
A.F<sub>1</sub>=10N,F<sub>2</sub>=10N
B. F<sub>1</sub>=20N,F<sub>2</sub>=20N
C. F<sub>1</sub>=2N,F<sub>2</sub>=6N
D. F<sub>1</sub>=20N,F<sub>2</sub>=30N
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证明:若函数f(x)在开区间I是下凸,则存在于f´-(x<sub>0</sub>)与f´+(x<sub>0</sub>),且f´-(x0)≤f´+(x<sub>0</sub>).
证明:若函数f(x)在开区间I是下凸,则<img src='https://img2.soutiyun.com/ask/2020-11-11/973977682582121.png' />存在于f´-(x<sub>0</sub>)与f´+(x<sub>0</sub>),且f´-(x0)≤f´+(x<sub>0</sub>).
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设函数f(x)在[0,1]上连续,且f(0)= f(1),证明一定存在x∈(0,)使得f(x<sub>0</sub>)= f(x<sub>0</sub>+).
设函数f(x)在[0,1]上连续,且f(0)= f(1),证明一定存在x∈(0,<img src='https://img2.soutiyun.com/ask/2020-12-20/977320815878019.png' />)使得f(x<sub>0</sub>)= f(x<sub>0</sub>+<img src='https://img2.soutiyun.com/ask/2020-12-20/977320902712985.png' />).
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证明:若函数f(x)在[a,b]是阶梯函数,即存在[a,b]的一个分法T,而f(x)在每个小开区间(x<sub>i</sub>-1,x<sub>i</sub>)都是常数(i=1,2,...n),则f(x)在[a,b]可积.
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若999个“1”异或的结果为F<sub>1</sub>,若999个“0”同或的结果为F<sub>2</sub>,则F<sub>1</sub>异或F<sub>2</sub>的结果为______。
A.0
B.1
C.不唯一
D.没意义
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证明:如果f<sub>1</sub>(x),f<sub>2</sub>(x),...,f<sub>s-1</sub>(x)的最大公因式存在,那么f<sub>1</sub>(x),f<sub>2</sub>(x),...
证明:如果f<sub>1</sub>(x),f<sub>2</sub>(x),...,f<sub>s-1</sub>(x)的最大公因式存在,那么f<sub>1</sub>(x),f<sub>2</sub>(x),...,f<sub>s-1</sub>(x),f<sub>s</sub>(x)的最大公因式也存在,且当f<sub>1</sub>(x),f<sub>2</sub>(x),...,f<sub>s</sub>(x)全不为零时有
<img src='https://img2.soutiyun.com/ask/2021-01-05/978706698167307.jpg' />
再利用上式证明,存在多项式u<sub>1</sub>(x),u<sub>2</sub>(x),...,u<sub>s</sub>(x),使
<img src='https://img2.soutiyun.com/ask/2021-01-05/978706734798402.jpg' />
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证明:(1)若且f在I上有界,则{f<sub>n</sub>}至多除有限项外,在I上是一致有界的;(2)若f<sub>n</sub>(x)→f(x)(n→
证明:(1)若<img src='https://img2.soutiyun.com/ask/2021-01-05/97872081021547.png' />且f在I上有界,则{f<sub>n</sub>}至多除有限项外,在I上是一致有界的;(2)若f<sub>n</sub>(x)→f(x)(n→∞).x∈I,且对每一个自然数n,f<sub>n</sub>在I上有界,则{f<sub>n</sub>}在I上一致有界.
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证明:若函数f(x,y)在R(a<sub>1</sub>≤x≤b<sub>1</sub>,a<sub>2</sub>≤y≤b<sub>2</sub>)连续,
证明:若函数f(x,y)在R(a<sub>1</sub>≤x≤b<sub>1</sub>,a<sub>2</sub>≤y≤b<sub>2</sub>)连续,
<img src='https://img2.soutiyun.com/ask/2020-11-14/974189428787492.png' />
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证明:函数f(x)在区间I单调,且x<sub>1</sub><x<sub>2</sub><x<sub>3</sub>,有[f(x<sub>3</sub>)-f(x<sub>2</sub>)][f(x<sub>2</sub>)-f(x<sub>1
证明:函数f(x)在区间I单调,<img src='https://img2.soutiyun.com/ask/2020-11-11/973942720007376.png' />且x<sub>1</sub><x<sub>2</sub><x<sub>3</sub>,有
[f(x<sub>3</sub>)-f(x<sub>2</sub>)][f(x<sub>2</sub>)-f(x<sub>1</sub>)]≥0.
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设f<sub>1</sub>(x), f<sub>2</sub>(x); g<sub>1</sub>(x), g<sub>2</sub>(x)都是数域K上的多项式,共中f<sub>1</sub>(x)≠0证明:如果g<sub>1</sub>(x)g<sub>2</sub>(x) | f<sub>1</sub>(x)f<sub>2</sub>(x), f<sub>1</sub>(x)|g<sub>1
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设f(x)在(0,+∞)上有意义,x<sub>1</sub>>0,x<sub>2</sub>>0.求证:(1)若单调减少,则;(2)若单调增加,则.
设f(x)在(0,+∞)上有意义,x<sub>1</sub>>0,x<sub>2</sub>>0.求证:
(1)若<img src='https://img2.soutiyun.com/ask/2021-01-12/979302582932847.png' />单调减少,则<img src='https://img2.soutiyun.com/ask/2021-01-12/979302592723407.png' />;
(2)若<img src='https://img2.soutiyun.com/ask/2021-01-12/979302582932847.png' />单调增加,则<img src='https://img2.soutiyun.com/ask/2021-01-12/97930261113346.png' />.
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设f(x)=d(x)f<sub>1</sub>(x),g(x)=d(x)g<sub>1</sub>(x)证明:若(f(x),g(x))=d(x)且f(x)和g(x)不全为零,则(f<sub>1</sub>(x),g<sub>1</sub>(x))=1;反之,若(f<sub>1</sub>(x),g<sub>1</sub>(x))=1,则d(x)是f(x)与g(x)的一个最大公因式。
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证明:(1)若函数f在[a,b]上可导,且f'(x)≥m,则(2)若函数f在[a,b]上可导,且(3)对任意实数x<sub>1
证明:(1)若函数f在[a,b]上可导,且f'(x)≥m,则
<img src='https://img2.soutiyun.com/ask/2021-02-04/98128598322409.png' />
(2)若函数f在[a,b]上可导,且
<img src='https://img2.soutiyun.com/ask/2021-02-04/981285989538451.png' />
(3)对任意实数x<sub>1</sub>,x<sub>2</sub>,都有
<img src='https://img2.soutiyun.com/ask/2021-02-04/981286001647143.png' />
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设f(x),g<sub>1</sub>(x),g<sub>2</sub>(x)∈C[x],证明:R(f,g<sub>1</sub>g<sub>2</sub>)=R(f,g<sub>1</sub>)R(f,g<sub>2</sub>)。
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已知基本放大器中频增益A<sub>1</sub>=10<sup>3</sup>极点频率f<sub>p1</sub>=1MHz,f<sub>p2</sub>=10MHz,f<sub>p3</sub>=100MHz,若要求闭环中频增益A<sub>f1</sub>=20dB,试用渐近波特图判断电路是否自激.
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将下列复数化为极坐标形式:(1) F<sub>1</sub>=-5-j5; (2) F<sub>2</sub>=-4+j3; (3) F<sub>3</sub>=20+j40; (4) F<sub>4</sub>=j10;(5) F<sub>5</sub>= -3;(6) F<sub>6</sub>=2.78-j9.20。