y=x^(3)+2x^(2)+3" at "(2,-1)

Draw graph of y=(x^(3)-2x^(2))/(3(x+1)^(2)) .

Draw graph of y=(x^(3)-2x^(2))/(3(x+1)^(2)) .

Draw graph of y=(x^(3)-2x^(2))/(3(x+1)^(2)) .

Draw graph of y=(x^(3)-2x^(2))/(3(x+1)^(2)) .

it x_(1)^(2) +2y_(1)^(2)+3z_(1)^(2)=x_(2)^(2)+2y_(2)^(2)+3z_(2)^(2)=x_(3)^(2)+2y_(3)^(2)+3z_(3)^(2)=2 " and " x_(2)x_(3) +2y_(2)y_(3)+3z_(2)z_(3)=x_(3)x_(1)+2y_(3)y_(1)+3z_(3)z_(1)=x_(1)x_(2)+2y_(1)y_(2)+3z_(1)z_(2)=1 Then find the value of |{:(x_(1),,y_(1),,z_(1)),(x_(2),,y_(2),,z_(2)),(x_(3),,y_(3),,z_(3)):}|

If y= {((3x-5) ^(2//3)(x ^(2) +1) ^(3//2))/((2x + 3)^(3//2) (3x ^(2) -1) ^(1//3))} then (dy)/(dx) =

if (x_ (1), y_ (1)), (x_ (2), y_ (2)), (x_ (3), y_ (3)) are vertices equilateral triangle such that (x_ (1) -2) ^ (2) + (y_ (1) -3) ^ (2) = (x_ (2) -2) ^ (2) + (y_ (2) -3) ^ (2) = (x_ (3) - 2) ^ (2) + (y_ (3) -3) ^ (2) then x_ (1) + x_ (2) + x_ (3) +2 (y_ (1) + y_ (2) + y_ (3) ))

Find each of the following products: (i) (x - 4)(x - 4) (ii) (2x - 3y)(2x - 3y) (iii) ((3)/(4) x - (5)/(6) y) ((3)/(4)x - (5)/(6) y) (iv) (x - (3)/(x)) (x - (3)/(x)) (v) ((1)/(3) x^(2) - 9) ((1)/(3) x^(2) - 9) (vi) ((1)/(2) y^(2) - (1)/(3) y) ((1)/(2) y^(2) - (1)/(3) y)

If A(x_(1), y_(1)), B(x_(2), y_(2)) , and, C(x_(3), y_(3)) are vertices of an equilateral triangle whose each side is equal to a, then prove that |(x_(1), y_(1), 2),(x_(2), y_(2), 2),(x_(3), y_(3), 2)|^(2) = 3a^(4) .