1-14 应用冲激信号的抽样特性,求下列表示式的函数值。-|||-(1) (int )_(-infty )^infty f(t-(t)_(0))delta (t)dt-|||-(2) (int )_(-infty )^infty f((t)_(0)-t)delta (t)dt-|||-(3) (int )_(-infty )^infty 8(t-(t)_(0))u(t-dfrac ({t)_(0)}(2))dt-|||-(4) (int )_(-infty )^infty 8(t-(t)_(0))u(t-2(t)_(0))dt-|||-(5) (int )_(-infty )^infty ((e)^-t+t)delta (t+2)dt-|||-(6) (int )_(-infty )^infty (t+sin t)delta (t-dfrac (pi )(6))dt-|||-(7) (int )_(-infty )^-infty (e)^-in7[ 8(t)-delta (t-(t)_(0))] dt

int_(-infty)^+infty delta(t-3)u(t-1), dt 的函数值是 (……)A. 0B. 1C. $\infty$D. 3

[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

8.[判断题]•标准正态分布Phi(x)=int_(-infty)^xvarphi(t)dt=(1)/(sqrt(2pi))int_(-infty)^xe^-(

[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)

【题目】-|||-设f(x)在 (-infty ,+infty ) 内连续,则 (int )_(2)^3f(x)dx+(int )_(3)^2f(t)dt+(i

6.证明 (x)=(int )_(1)^xsqrt (1+{t)^3}dt 在 [ -1,+infty ) 上是单调增加函数,并求 ((f)^-1)(0).

6.证明 (x)=(int )_(1)^xsqrt (1+{t)^3}dt 在 [ -1,+infty ) 上是单调增加函数,并求 ((f)^-1)(0).

9.设函数f(x)连续, (x)=(int )_(0)^sin xf(t(x)^2)dt-|||-(1)求F`(x);-|||-(2)讨论函数F`(x )的连续

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.计算题求函数f(t)=}sin t,|t|leqpi0,|t|>pi的傅氏变换，并证明int_(0)^+infty(sinomegapisinomega t