Question

谁能帮忙做一下？求极限，求积分的题目~谢谢

Answer 1

(1)

∫(-1->1) (x^3+2x^2) dx
=∫(-1->1) 2x^2 dx
=4∫(0->1) x^2 dx
=(4/3)[x^3]|(0->1)
=4/3
(2)
∫(-1->1) (x^3+x^2) dx
=∫(-1->1) x^2 dx
=2∫(0->1) x^2 dx
=(2/3)[x^3]|(0->1)
=2/3
(3)
∫(0->1) (x^3+3x^2) dx
=[(1/4)x^4 +x^3]|(0->1)
=5/4
(4)
lim(n->无穷) (1+1/n)^(2n)= e^2
(5)
lim(n->无穷) (1+1/n)^(3n)= e^3
(6)
lim(n->无穷) (1+1/n)^(4n)= e^4