Question

比較下列各題中兩個(gè)值的大小:

(1)1.7².5,1.7³;  (2)0.8^-0.1,0.8^-0.2.

Answer 1

思路分析:

此題考查指數(shù)函數(shù)的單調(diào)性.對y=a^x,當(dāng)0＜a＜1時(shí),函數(shù)為減函數(shù);當(dāng)a＞1時(shí),函數(shù)為增函數(shù).結(jié)合相應(yīng)圖象可順利解題.

解:(1)1.7^2.5與1.7³的底數(shù)是1.7,它們可以看成函數(shù)y=1.7^x,圖象如圖2-1-6,當(dāng)x=2.5和3時(shí)的函數(shù)值.因?yàn)?.7＞1,所以函數(shù)y=1.7^x在R上是增函數(shù),而2.5＜3,所以1.7^2.5＜1.7³.

 

(2)0.8^-0.1與0.8^-0.2的底數(shù)是0.8,它們可以看成函數(shù)y=0.8^x,圖象如圖2-1-7,當(dāng)x=-0.1和-0.2時(shí)的函數(shù)值.因?yàn)?＜0.8＜1,所以函數(shù)y=0.8^x在R上是減函數(shù),而-0.1＞-0.2,所以0.8^-0.1＜0.8^-0.2.