Question

高数 ，曲线的渐进线

高数 ，曲线的渐进线这道题目怎么写呀

Answer 1

简单计算一下即可，答案如图所示

Answer 2

望采纳

Answer 3

嗯嗯

Answer 4

x趋于π/2时，极限为正无穷大，所以，x= π/2是一条水平渐进线。
x趋于—π/2时，极限为负无穷大，所以，x=— π/2也是一条水平渐进线。
共2条

Answer 5

设 y = xarctanx 的渐近线是 y = kx + b
则 k1 = lim<x→+∞>y/x = lim<x→+∞>arctanx = π/2,
b1 = lim<x→+∞>(y-k1x) = lim<x→+∞>x(arctanx-π/2)
= lim<x→+∞>(arctanx-π/2)/(1/x) (0/0)
= lim<x→+∞>[1/(1+x^2)]/(-1/x^2) = lim<x→+∞>[-x^2/(1+x^2)] = -1，
一条渐近线是 y = (π/2)x - 1 ;
k2 = lim<x→-∞>y/x = lim<x→-∞>arctanx = -π/2,
b2 = lim<x→-∞>(y-k1x) = lim<x→-∞>x(arctanx-π/2)
= lim<x→-∞>(arctanx-π/2)/(1/x) (0/0)
= lim<x→-∞>[1/(1+x^2)]/(-1/x^2) = lim<x→-∞>[-x^2/(1+x^2)] = -1;
另一条渐近线是 y = -(π/2)x - 1