Question

求解以下问题

y=sec x的周期是什么 y=sec x是奇函数还是偶函数 y截距是 y=sec x 有无x截距 y=sec x的所有垂直渐近线是x=___+___k

Answer 1

令：v=y/x,y=xv,dy=vdx+xdv dy/dx = -(y^2-2xy)/x^2 (vdx+xdv)/dx = 2v - v^2 v+xdv/dx = 2v - v^2 xdv/dx = v - v^2 dv/[v(1 - v)] = dx/x ∫dv/[v(1 - v)] = ∫dx/x ∫dv/v + ∫dv/(1 - v)] = ∫dx/x lnv - ln(1-v) = lnx ln(v/(1-v))=lnx+lnc v/(1-v)=cx (y/x)/(1-(y/x))=cx y/(x-y)=cx y=cx(x-y)