((1+x²)∧1/3 -1)/cosx-1 x趋向0时,求极限
问题描述:
((1+x²)∧1/3 -1)/cosx-1 x趋向0时,求极限
答
x趋向0时 1-cosx等价于1/2x^2
所以x趋向0时 cosx-1等价于-1/2x^2
又x趋于0式,(1+m)^1/n-1等价于m/n
所以当x趋于时,(1+x²)∧1/3 -1等价于x^2/3
所以((1+x²)∧1/3 -1)/cosx-1 x趋向0时,极限是-2/3