4.20若已知 (t)arrow F(jomega ) ,试求下列函数的频谱。-|||-(1)tf(2t)-|||-(2) (t-2)f(t)-|||-(3) dfrac (df(t))(dt)-|||-(4) f(1-t)-|||-(5) (1-t)f(1-t)-|||-(6) f(2t-5)-|||-(7)(int )_(-infty )^1-dfrac (1{2)t}f(t)dt-|||-(8) ^itf(3-2t)-|||-(9) dfrac (df(t))(dt)neq dfrac (1)(pi t)

[例18]设f(x )连续,试求下列函数的导数.-|||-(1)f(t)dt;-|||-(2) (int )_(0)^x(x-t)f(t)dt ;-|||-(3

[例18] 设f(x)连续,试求下列函数的导数.-|||-(1) (int )_({e)^x}f(t)dt;-|||-(2) (int )_(0)^x(x-t)

2-13 求下列各函数f1 (t)与f2(t )的卷积 _(1)(t)*(f)_(2)(t)-|||-(1) _(1)(t)=u(t), _(2)(t)=(e)

求曲线=(t)_(2), =2t, =dfrac (1)(2)(t)^2在对应于=(t)_(2), =2t, =dfrac (1)(2)(t)^2点的切线方程和

2-9 求下列微分方程描述的系统冲激响应h(t)和阶跃响应g(t)。-|||-(1) dfrac (d)(dt)r(t)+3f(t)=2dfrac (d)(dt

求曲线 =2t, =(t)^2, =dfrac (2)(3)(t)^3 上对应于=2t, =(t)^2, =dfrac (2)(3)(t)^3 的点处的切线及法

2.17 求下列函数的卷积积分 _(1)(t)*(f)_(2)(t)-|||-(1) _(1)(t)=tg(t) _(2)(t)=g(t)-|||-(2) _(

设 f 在[0,1]上是单调增正值函数，令=dfrac ({int )_(0)^1tf(t)dt}({{int )_(0)^1}f(t)dt}，证明：=dfra

2.17 求 下列函数的卷积积分 _(1)(t)*(f)_(2)(t) o-|||-(1) _(1)(t)=tg(t) _(2)(t)=g(t)-|||-(2)

2.17 求下列函数的卷积积分 _(1)(t)*(f)_(2)(t) o-|||-(1) _(1)(t)=tg(t) ,_(2)(t)=e(t)-|||-(2)