152 MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



7.19 Limiting Values of Products. 



if c>o. 

 Limit 7 c\ c c 



if a, bj c are all positive. 



Limit[~jra(w + i) (m + 2) . . . . . (m + n i)}"| 2 



if w>o. 



7.20 Maxima and Minima. 



7.201 Functions of One Variable, y = f(x) is a maximum or minimum for the 



values of x satisfying the equation, f(x) = ^ = o, 



ox 



provided that f'(x) is continuous for these values of x. 



7.202 If, for x = a, /'(a) = o, 



y = f( a ) is a maximum if J"(a)<o 



y = }() is a minimum if f"(a)>o. 

 Example: 



/'w 



. r + ax -f 

 ^'(*) = o when ^ 



.// / >. 2^J OL)X 2(X 



(x* + ax + 0) 3 

 For x = +VJS," /"(*) = ^ z^ Maximum, 



