[" (19) The smallest value of the "],[" Constant "m>0" jor which "],[f(x)=9mx-1+1/x geqslant0" dadaxia "],[" is "],[" 1) "(1)/(9)" 2) "(1)/(16)" 3) "(1)/(36)" ( "y" ) "81]

The smallest value of the constant m>0 for which f(x)=9mx-1+(1)/(x)>=0 for all x>0, is

The smallest value of of the constant m gt 0 for which f(x) = 9mx - 1 + (1)/(x)ge 0 for all x gt 0 , is

[{(-1/3)^2}^(-2)]^(-1) = (a) 1/(81) (b) 1/9 (c) -1/(81) (d) -1/9

[{(-1/3)^2}^(-2)]^(-1) = (a) 1/(81) (b) 1/9 (c) -1/(81) (d) -1/9

Prove that: 9(3)/(2)quad -3x5^(0)-((1)/(81))^(-(1)/(2))=15

(1)/(2) + (1)/(4) + (1)/(8) + (1)/(16) + ….. = x , (1)/(3) + (1)/(9) + (1)/(27) + (1)/(81) + … = y, then

[" 24.If "M(x_(0),y_(0))" is the point on the curve "3x^(2)-4y^(2)=72" ,whic "],[" is nearest to the line "3x+2y+1=0" ,then the value "o],[[x_(0)+y_(0)" ) is equal to "," (2) "-3," (3) "9," (4) "-9],[" (1) "3," (3) "]]