Question

求教一道高数填空题,要有解题步骤哦

Answer 1

Lim(n→∞)∫(上1下0) x^n√(1+x^2)dx =

∫(上1下0) Lim(n→∞) x^n√(1+x^2)dx = 0 ,

Lebesgue控制收敛定理.

方法二：0 ≤ Lim(n→∞)∫(上1下0) x^n√(1+x^2) dx ≤Lim(n→∞)∫(上1下0) 2(x^n) dx = Lim(n→∞) 2/(1+n) = 0