f(x)=x^a[cos(1/x)] (x不等于0) =0 (x=0),其导数在x=0处连续,求a的取值范围

来源：学生作业帮助网编辑：作业帮时间：2024/05/29 12:26:03

f(x)=x^a[cos(1/x)] (x不等于0) =0 (x=0),其导数在x=0处连续,求a的取值范围
f(x)=x^a[cos(1/x)] (x不等于0) =0 (x=0),其导数在x=0处连续,求a的取值范围

f(x)=x^a[cos(1/x)] (x不等于0) =0 (x=0),其导数在x=0处连续,求a的取值范围
f‘(x)=x^a[cos(1/x)] =ax^(a-1)[cos(1/x)] +x^(a-2)[sin(1/x)]=x^(a-2)[axcos(1/x)+[sin(1/x)]
f'(0)=[x^a[cos(1/x)]-0]/x=limx^(a-1)[cos(1/x)]
要使f'(0)存在,a-1>0,这时f'(0)=0
要使导数在x=0处连续,limf‘(x)=0,a-2>0
故a>2

f'(sin x)=1-cos x 求f''(x) f(sinx)=1+cos(2x),求f(x), 函数f(x)=cos((根号三x)+A)(0 已知f(x)=cos(-2x+a)(-π 若函数f(x)=cos(x+a)(0 函数f(x){lg(x+1),x>0 cosπx/2,x函数f(x)={lg(x+1),x>0 cosπx/2,x 设函数f(x)可导,则 [sin f(x)]'= (A)sin f'(x) (B)cos f'(x) (C)f'(x)cos f(x) (D)f(x)cos f'(x) f(sin x)=cos 2x +1 求 f(cos x) f(x)=cos x(x+|sin x| ),则在x=0处有.(A)f'(X)=2 (B)f'(x) =1 (C)f'(x) =0 (D)f'(x) 不可导. 设函数f ( x )可导,y= f ( x )cos f ( x )的导数为（）.A:y'= f′( x )cos f ( x )- f( x )sin (f ( x )) f′( x ) B:y ′=-f′( x )sin f ( x ) C:y ′= f′( x )cos f ( x )+ f( x )sin (f ( x )) f′( x ) D:y ′= f′( x )cos f ( x )-f( x )s f(x)=cos/x求导! 化简f(x)=cos x*sin2x 如果f(cos x)=sin 3x,那么f(sin x)等于A.sin 3x B.-sin 3x Ccos 3x D-cos 3x 设函数f(x)=a*b,其中向量a=(2cos x,1),b=(cos x,根号3 sin 2x),x属于(-30,30度),f(s)=3/4,求cos(2x) 向量a=(sin(ωx)+cos(ωx),1),b=(f(x),sinωx),其中0 已知函数f(x)=2cos²x-2acosx-(2a+1),求f(x)的最小值当x=a时,f（x）=sin x - 2cos x取得最大值,则cos a =? 设f(sin x/2 )-1+cos x ,求f(x)、f(cos x/2 ).