lim(x->0){[f(3t)-f(-t)]/(2t)}
=lim(x->0){[(3/2)(f(3t)-f(0))/(3t)]+[(1/2)(f(-t)-f(0))/(-t)]}
=(3/2)lim(x->0)[f(3t)-f(0))/(3t)]+(1/2)lim(x->0)[f(-t)-f(0))/(-t)]
=(3/2)f'(0)+(1/2)f'(0)
=(3/2)*1+(1/2)*1
=2.
设f'(0)=1,则x趋向0时lim(f(3t)-f(-t))/2t =
1个回答
相关问题
-
设F(x)=∫(0趋向x) [(x-t)f(t)dt]/(sinx)^2 求lim(x趋向0)F(x),f(0)存在,
-
lim(x趋向于0时)∫(x 0)tf(x-t)dt为什么=lim(x趋向于0时)∫(x 0)(x-t)f(t)dt 其
-
若f(x)=e^(-x^2),则lim t→ 0 [f(1-2t)-f(1)]/t 等于多少?
-
设f(x)连续且f(0)=0,f'(0)=1 计算lim(x->0)=∫(t*f(x^2-t^2)dt)\x^4 积分的
-
设函数f（x）在x0可导，则limt→0f(x0+t) −f(x0−3t)t=（ ）
-
设f（u）在u=0的领域内连续,且lim（n趋向于0）f（u）/u=A,求lim（x趋向于0）d/dx∫【0,1】f（t
-
设连续函数f(x)满足f(x)+2∫[0→x]f(t)d t=x^2,则f(x)=__________.
-
设F(X)=∫(2x,0)t^2sin(t^2)dt,则F'(X)=?
-
设f(x)连续,且f(0)0,求极限lim(x~0)∫x上0下(x-t)f(t)dt/x∫x上0下(x-t)dt
-
设函数f x连续 ∫[0,x^2-1] f(t) dt=2x(x>0)则f(3)=