The Problems of functions and Graphs?

Lau

2015-09-12 7:49 pm

Please find the range of the function of the questions of 19
and explain it by algebraically
Thank you very much

回答 (1)

螞蟻雄兵

2015-09-13 12:32 am

✔ 最佳答案

Sol
1－x^2=0
(x－1)(x+1)=0
x=1 or x=－1
x^2=0
x=0
定義域=｛x｜x<>+/-1｝
f(x)=x^2/(1－x^2)=－1+1/(1－x^2)
lim(x->0)_x^2/(1－x^2)=0
lim(x->∞)_x^2/(1－x^2)=1
lim(x->－∞)_x^2/(1－x^2)=－1
lim(x->－1-)_x^2/(1－x^2)=－∞
lim(x->－1+)_x^2/(1－x^2)=∞
lim(x->1-)_x^2/(1－x^2)=∞
lim(x->1+)_x^2/(1－x^2)=－∞

－１　　　－∞　∞　　０　　　∞　－∞ １
───────＊───＊────＊───────
－∞　　　　　－１　　０　　　　１　　　　　　∞
值域=(－∞，－1)U[0，∞)

👍 1 👎 0