求a,b使(x>2+1)/(x+1)+ax+b,当x趋向于无穷大时为无穷小
问题描述:
求a,b使(x>2+1)/(x+1)+ax+b,当x趋向于无穷大时为无穷小
答
∵lim(x->∞)(x^2+1)/(x+1) -ax-b = 0∴0=lim(x->∞)[(x^2+1)/(x+1) -ax-b ] / x=lim(x->∞)[(x+1/x)/(x+1) -a-b/x=lim(x->∞)[(1+1/x^2)/(1+1/x) -a-b/x= 1 - a - 0= 1-a∴ a = 1∴lim(x->∞)(x^2+1)/(x+...