数学题,函数的极限lim (x²/x²-1)3x次方 2.lim(tanx)tan2x次方x→无穷大
来源:学生作业帮 编辑:大师作文网作业帮 分类:数学作业 时间:2024/09/23 05:26:08
数学题,函数的极限
lim (x²/x²-1)3x次方 2.lim(tanx)tan2x次方
x→无穷大 x→π/4
lim (x²/x²-1)3x次方 2.lim(tanx)tan2x次方
x→无穷大 x→π/4
lim(x->∞) [x²/(x²-1)]^3x
=lim(x->∞) [1+1/(x²-1)]^3x
=lim(x->∞) {[1+1/(x²-1)]^(x²-1)}^[(3x)/(x²-1)]
∵lim(x->∞) {[1+1/(x²-1)]^(x²-1)}=e
lim(x->∞) [(3x)/(x²-1)] = 0
=e^0
=1
2.
令:tanx = t ,tan2x = 2t/(1-t²) ,x→π/4 ,t->1
lim( x→π/4) (tanx)^(tan2x)
=lim( t→1) (t)^[2t/(1-t²)]
=lim( t→1) [1+(t-1)]^{ 1/(t-1) * [2t(t-1)/(1-t²)] }
=lim( t→1) {[1+(t-1)]^{ 1/(t-1)}^[-2t/(1+t)]
∵lim( t→1) {[1+(t-1)]^{ 1/(t-1)} = e
lim( t→1) [-2t/(1+t)] = -1
= e^(-1)
= 1/e
=lim(x->∞) [1+1/(x²-1)]^3x
=lim(x->∞) {[1+1/(x²-1)]^(x²-1)}^[(3x)/(x²-1)]
∵lim(x->∞) {[1+1/(x²-1)]^(x²-1)}=e
lim(x->∞) [(3x)/(x²-1)] = 0
=e^0
=1
2.
令:tanx = t ,tan2x = 2t/(1-t²) ,x→π/4 ,t->1
lim( x→π/4) (tanx)^(tan2x)
=lim( t→1) (t)^[2t/(1-t²)]
=lim( t→1) [1+(t-1)]^{ 1/(t-1) * [2t(t-1)/(1-t²)] }
=lim( t→1) {[1+(t-1)]^{ 1/(t-1)}^[-2t/(1+t)]
∵lim( t→1) {[1+(t-1)]^{ 1/(t-1)} = e
lim( t→1) [-2t/(1+t)] = -1
= e^(-1)
= 1/e
lim(1+x/x)的3x次方的极限.x趋向无穷大
lim x趋近于无穷大 sin3次方x分之tanx-sinx的极限
lim(x→-无穷大)10的x次方 的极限是什么
求极限LIM(3X²-2X-1)/(2X²-3X+1) (X趋向无穷大)
lim(x→∞)[(3+x)/(6+x)]的[(x-1)/2]次方的极限
用洛必达法则求lim x→0 tanx-x /(x²sinx)的极限
lim X趋向无穷大时,求(2x-1/2x+1)的X+1次方的极限
lim X趋向无穷大时,求(2x-1/2x+1)的X次方的极限
请问,lim X趋向无穷大时,求(2x-1/2x+1)的X次方的极限
高数求极限 lim(tanx)^tan2x ,x→π/4
lim x→0.25派 (tanx)∧tan2x 求极限
求极限 lim(tanx)^tan2x ,x→∏/4