" (v) "y=10-x^(2)-x^(3)-(1)/(4)x^(4)

Find for what values of x the following functions are maximum and minimum Also find the corresponding maximum and minimum values : y=10-x^(2)-x^(3)-(1)/(4)x^(4)

If |x|lt1 and y=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+... , then x =

If |x|lt1 and y=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+... , then x =

If |(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x)|=3 then find the value of |(x^(3)-1,0,x-x^(4)),(0,x-x^(4),x^(3)-1),(x-x^(4),x^(3)-1,0)|

If |{:(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x):}| =3 then the value of |{:(x^(3)-1,0,x-x^(4)),(0,x-x^(4),x^(3)-1),(x-x^(4),x^(3)-1,0):}| is

If |{:(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x):}| =3 then the value of |{:(x^(3)-1,0,x-x^(4)),(0,x-x^(4),x^(3)-1),(x-x^(4),x^(3)-1,0):}| is

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)

(1)/(3)x+y=(10)/(3),2x+(1)/(4)y=(11)/(4)

Show that: (x^(2)+y^(2))^(5)=(x^(5)-10x^(3)y^(2)+5xy^(4))^(2)+(5x^(4)-10x^(2)y^(3)+y^(5))^(2)