x趋于无穷,(x^2+a^2/x^2-a^2)^(x^2)的极限
2个回答

令m=x²

则m→∞

原式=[(m-a²+2a²)/(m-a²)]^m

=[1+2a²/(m-a²)]^m

令2a²/(m-a²)=1/n

则m→∞有n→∞

m=2na²+a²

原式=(1+1/n)^(2na²+a²)

=(1+1/n)^(2na²)*(1+1/n)^a²

=[(1+1/n)^n]^2a²*(1+1/n)^a²

n→∞,a是常数,所以(1+1/n)^a²极限是1

(1+1/n)^n极限是e

所以原来极限=e^(2a²)