" (i) "9^(x+2)-6x3^(x+1)+1=0

9^(x+2)-6xx3^(x+1)+1=0

Solve for x,9^(x+2)-6.3^(x+1)+1=0

The number of negative roots of 9^(x +2) - 6 (3^(x +1)) + 1 = 0 is

If 1,1, alpha are the roots of x ^(3) -6x ^(2) + 9x- 4 =0 then find 'alpha '.

9x^2-6x+1 -: (3x-1)

For x in(0,1) arrange f_(1)(x) = (1)/(9-x^(2)), f_(2)(x) = (1)/(9-2x^(2)) and f_(3)(x) = (1)/(9-x^(2)-x^(3)) in ascending order and hence prove that 1/6 ln2 lt int_(0)^(1)(1)/(9-x^(2)-x^(3)) dx lt (1)/(6sqrt(2)) ln 5 .

For x in(0,1) arrange f_(1)(x) = (1)/(9-x^(2)), f_(2)(x) = (1)/(9-2x^(2)) and f_(3)(x) = (1)/(9-x^(2)-x^(3)) in ascending order and hence prove that 1/6 ln2 lt int_(0)^(1)(1)/(9-x^(2)-x^(3)) dx lt (1)/(6sqrt(2)) ln 5 .

Compute Lt_(x to 3) (x^2 - 9)/(x^3 - 6x^2 + 9x + 1)

lim_(x rarr3)(x^(2)-9)/(x^(3)-6x^(2)+9x+1)