(x^2cos^2x-sin^2x)/x^2cos^2xsin^2x （x->0）lim (x^2cos^2x-sin^2x)/x^2cos^2xsin^2x （x->0）=lim [cos^2x-(sin^2x/x^2)]/cos^2xsin^2x=lim (cos^2x-1)/sin^2x=lim -sin^2x/sin^2x=-1这样解错在哪啊?小弟感激不尽

来源：学生作业帮助网 编辑：作业帮 时间：2024/05/05 13:58:39
(x^2cos^2x-sin^2x)/x^2cos^2xsin^2x （x->0）lim (x^2cos^2x-sin^2x)/x^2cos^2xsin^2x （x->0）=lim [cos^2x-(sin^2x/x^2)]/cos^2xsin^2x=lim (cos^2x-1)/sin^2x=lim -sin^2x/sin^2x=-1这样解错在哪啊?小弟感激不尽
xTMo@+{[cң!?$ r@mRT1$HTMҨ 6Q )C[}{ovxeB6z'cYYO< @w##+'wZ)!N36i*7p LdweZi@A:J0pξ77^UVs2VȲ9>2;s\V{iJ&uo+w wuHָnS=N0xː;cz[gTMvsݠ@*) rpBͶ,p ~QIبD0*ZK(tK ܴQ&;e[#^Qeث\Fx/}ӳΧcw܆΅7Mp ]ϸUH"Q]'^w*=M#Y]GR>e2M#YQAFey@SSI 5.-HX81,Te}{6sCSx%y3#EqDn"h,Xf#I{W={

(x^2cos^2x-sin^2x)/x^2cos^2xsin^2x （x->0）lim (x^2cos^2x-sin^2x)/x^2cos^2xsin^2x （x->0）=lim [cos^2x-(sin^2x/x^2)]/cos^2xsin^2x=lim (cos^2x-1)/sin^2x=lim -sin^2x/sin^2x=-1这样解错在哪啊?小弟感激不尽
(x^2cos^2x-sin^2x)/x^2cos^2xsin^2x （x->0）
lim (x^2cos^2x-sin^2x)/x^2cos^2xsin^2x （x->0）
=lim [cos^2x-(sin^2x/x^2)]/cos^2xsin^2x
=lim (cos^2x-1)/sin^2x
=lim -sin^2x/sin^2x
=-1
这样解错在哪啊?小弟感激不尽

(x^2cos^2x-sin^2x)/x^2cos^2xsin^2x （x->0）lim (x^2cos^2x-sin^2x)/x^2cos^2xsin^2x （x->0）=lim [cos^2x-(sin^2x/x^2)]/cos^2xsin^2x=lim (cos^2x-1)/sin^2x=lim -sin^2x/sin^2x=-1这样解错在哪啊?小弟感激不尽
从第二步到第三步是不对的.即
lim [cos^2x-(sin^2x/x^2)]/cos^2xsin^2x
=lim (cos^2x-1)/sin^2x
是不对的.如果这样做,就默认了
lim [cos^2x-(sin^2x)/x^2]/sin^2x
=[lim cos^2x-lim (sin^2x)/x^2]/lim(sin^2x)
但如果这样,因为 lim(sin^2x)=0,此时分母为0,分式无意义,也就是说此时极限的四则运算不成立,因此不能用.
不知道你学过洛必达法则没有,用洛必达法则是比较简单的.
原极限
=lim [cos^2x-(sin^2x/x^2)]/sin^2x
=lim (1/tan^2x - 1/x^2)
=lim (x^2-tan^2x)/(x^2tan^2x) (lim tan^2x/x^2=1)
=lim (x^2-tan^2x)/x^4
=lim (x+tanx)/x * lim (x-tanx)/x^3
=2lim (x-tanx)/x^3 (洛必达法则)
=2lim (1-sec^2x)/(3x^2)
=2lim (-tan^2x)/(3x^2)
=-2/3
即原式 = -2/3.

lim (x^2cos^2x-sin^2x)/x^2cos^2xsin^2x
=lim [cos^2x-(sin^2x/x^2)]/cos^2xsin^2x
mistake....

已知tan=2,求(cos x+sin x)/(cos x-sin x)+sin^2x 化简(sin x+cos x-1)(sin x-cos x+1)/sin 2x 2cos x (sin x -cos x)+1 y=2cos x (sin x+cos x) 化简sin(x)cos(x)cos(2x) 化简sin(x)cos(x)cos(2x) sin x cos x cos 2x 化简 化简 cos^2(x)*sin^2(x)-sin^2(x) 化简 cos^(2)(x)*sin^(2)(x)-sin^(2)(x) (sin^2x+cos^2x )(sin^2x-cos^2x)怎么得sin^2x-cos^2x? 化简sin^4x-sin^2x+cos^2x 化简:sin^4 x-sin^2 x+cos^2 x 已知sin(x)+3cos(x)=2,求sin(x)-cos(x)/sin(x)+cos(x)=? sin(x/2)cos(x/2)= 化简sin^4x+cos^2x sin[cos^2(x^3+x)],求导 y=(sin x + COS x)^2 化简(sin^2x-cos^4x+cos^2x-sin^4x)/(sin^2x-cos^6x+cos^2x-sin^6x)