[sqrt(9x^(2)+6x+1)<2-x" then "],[x in(-(3)/(2),(1)/(4))quad " 2) "x in(-(3)/(2),(1)/(4)]],[x in[-(3)/(2),(1)/(4))quad " 4) "x<(1)/(4)]

lim_(x rarr3)((x^(2)-9-sqrt(x^(2)-6x+9)))/(|x-1|-2)

(1)/(log_(3)(x+1))<(1)/(2log_(9)sqrt(x^(2)+6x+9))

Find the range of f(x)=sqrt(1-sqrt(x^(2)-6x+9))

lim_(x rarr oo)((sqrt(1+25x^(2))+sqrt(9x^(2)-1))/(sqrt(1+25x^(2))-sqrt(9x^(2)-1)))=

underset(x to oo)lim (sqrt(1+25x^(2))+sqrt(9x^(2)-1))/(sqrt(1+25x^(2))-sqrt(9x^(2)-1))

Find all possible values of expression sqrt(1-sqrt(x^(2)-6x+9)).

Find all possible values of expression sqrt(1-sqrt(x^(2)-6x+9)).

Find all possible values of expression sqrt(1-sqrt(x^(2)-6x+9)).

Using properties of proportion, solve for x : (i) (sqrt(x + 5) + sqrt(x - 16))/ (sqrt(x + 5) - sqrt(x - 16)) = (7)/(3) (ii) (sqrt(x + 1) + sqrt(x - 1))/ (sqrt(x + 1) - sqrt(x - 1)) = (4x -1)/(2) . (iii) (3x + sqrt(9x^(2) -5))/(3x - sqrt(9x^(2) -5)) = 5 .

The value of int(dx)/((x^(2)-6x+9)sqrt(x^(2)-6x+4)) is