Find `(x+y)-:(x-y),` if `x=2/3, y=3/2` (ii) `x=2/5, y=1/2` `x=5/4, y=(-1)/3`

Find (x+y)+(x-y), if x=(5)/(4),y=(-1)/(3) (ii) x=(2)/(7),y=(4)/(3)( iii) x=(1)/(4),y=(3)/(2)

Find (dy)/(dx), when (i) y=sqrt(x) (ii) y=x^(5)+x^(4)+7 (iii) y=x^(2)+4x^(-1//2)-3x^(-2)

Find x and y if: (i) (x + 1,y-2) = (3,1) (ii) (x + 2,4)= (5,2x+y)

Find the S.D. between the lines : (i) (x)/(2) = (y)/(-3) = (z)/(1) and (x -2)/(3) = (y - 1)/(-5) = (z + 4)/(2) (ii) (x -1)/(2) = (y - 2)/(3) = (z - 3)/(2) and (x + 1)/(3) = (y - 1)/(2) = (z - 1)/(5) (iii) (x + 1)/(7) = (y + 1)/(-6) = (z + 1)/(1) and (x -3)/(1) = (y -5)/(-2) = (z - 7)/(1) (iv) (x - 3)/(3) = (y - 8)/(-1) = (z-3)/(1) and (x + 3)/(-3) = (y +7)/(2) = (z -6)/(4) .

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)

Show that the lines : (i) (x -5)/(7) = (y + 2)/(-5) = (z)/(1) " " and (x)/(1) = (y)/(2) = (z)/(3) (ii) (x - 3)/(2) = (y + 1)/(-3) = (z - 2)/(4) and (x + 2)/(2) = (y - 4)/(4) = (z + 5)/(2) are perpendicular to each other .

Find (dy)/(dx) for the following : (i) y=x^(7//2) (ii) y=x^(-3) (iii) y=x (iv) y=x^(5)+x^(3)+4x^(1//2)+7 (v) y=5x^(4)+6x^(3//2)+9x (vi) y=ax^(2)+bx+C (Vii) y=3x^(5)-3x-1/x

Solve for x and y 2/(3x+2y)+3/(3x-2y)=17/5,5/(3x+2y)+1/(3x+2y)=6/5