lim（1/x^2 - cot^2 x ) (x趋近于0) 用洛必达法定则

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lim（1/x^2 - cot^2 x ) (x趋近于0) 用洛必达法定则
lim（1/x^2 - cot^2 x ) (x趋近于0) 用洛必达法定则

lim（1/x^2 - cot^2 x ) (x趋近于0) 用洛必达法定则
原式=lim(1/x^2-cos^2x/sin^2x)
=lim(sin^2x-x^2*cos^2x)/(x^2*sin^2x)
=lim(sin^2x-x^2*cos^2x)/(x^4)
=lim[cos^2x(tan^2x-x^2)]/x^4
=lim(tan^2x-x^2)/x^4
=lim(2tanx*sec^2x-2x)/4x^3
=lim(sec^4x+2sec^2x*tan^2x-1)/6x^2
=lim(sec^4x-1)/6x^2+lim(2tan^2x*sec^2x)/6^2x
=lim[(sec^2x+1)(sec^2x-1)]/6x^2+1/3
=lim(sec^2x+1)*tan^2x/6x^2+1/3
=lim(sec^2x+1)/6+1/3
=1/3+1/3
=2/3

lim x→0 (cot x)^tan 2x= 当x正向趋近于1时,lim((ln (x-1)-x)/cot(派/(2x))) lim(cosx)^cot^2x当x趋近于0 lim x趋向0 1/x∧2— cot∧2x 求极限 lim（1/x^2 - cot^2 x ) (x趋近于0) 用洛必达法定则求lim(x->0)(1+3(tan^2)x)^((cot^2)x) lim(x→0)(1+3tan^2(x))^cot^2(x)=? 求极限LIM（趋近与0）(cot^2 *x-1/x^2)nannan na 求极限LIM（趋近与0）(cot^2 *x-1/x^2)急 lim（x→0）=(1/x^2-cot^2x)lim(x→∞)=[(2+x)e^(1/x)-x] 求极限 lim [ln（x-1) - x] cot π/2x x→1+lim [ln（x-1) - x] cot π/2x x→1+ 好像不太对啊，两位 x趋向1负时,求lim【ln(1-x)+tan派/2*x】/cot派*x,谢谢 x趋向于0 lim(1+tanx)^1-2cot 求极限 cot^2x+1 是多少cot平方x +1 x趋向0 lim(cot x- 1/x)=? lim x趋于pai/2 (x-pai/2) cot 2x lim (arcsinx/x)^{[cot(x)]^2} x→0如题求极限 lim（1/x²-cot²x）