三道题都是很基础的题,关键在于变换!
答案如下:
(1):3;
(2):-2/派;
(3):h;
解题步骤如下:
lim(x->pi/2)tgx/tg3x=lim(x->pi/2)sinx*cos3x/sin3x*cosx=lim(x->pi/2)-cos3x/cosx=lim(x->pi/2)-3sin3x/sinx=3;
lim(x->1)(1-x)(tg派x/2)=lim(x->1)(1-x)(sinpix/2)/(cospix/2)=lim(x->1)(1-x)/(conpix/2)=-2/pi.
lim(x->∞)x(sinh/x)=lim(x->∞)(sinh/x)/(1/x)=lim(x->∞)(h/x)/(1/x)=h.