214 
CALCULUS 
and the limit is obvious. Or, the method of series may be used: 
Va 2 + l = x(l + 4V = *1 1 \ + 1» etc - 
EXERCISES ON CHAPTER X 
Determine in the most convenient manner possible each of the 
following limits. 
1. lim xe~ x2 . 2. lim x n e~ xi . 
4. lim 
log x 
*=oo 1 + x -j- x 2 
5. lim 
3. lim x n e~ ax , 0 < a. 
*=oo 
(log xY 
x=» 4- x + x°- -)- x 5 
//£W+l\ /^QpT 
6. lim x n e~ x log x. Suggestion : x n e~ x log x = f ] f —)• 
*=oo ^ €, x J QC J 
7. limx n e~ x (logx) 2 . 8. limæ a ( log - ] » |0<a, 
x=*> x==co x J lO</3. 
9. lim er x cot -1 x. 
e * 
10. lim 
X=-°0 X 
11. lim (sin æ) tanx . 
. 7T 
*=2 
X=CO