If `y=(1/x)^x` then `y_2 (1)`

If y=xe^(-1//x)," then "x^(3)y_(2)-xy_(1)=

If y=(tan^(-1)x)^(2), then prove that (1+x^(2))^(2)y_(2)+2x(1+x^(2))y_(1)=2

If graph of y=(x-1)(x-2) is then draw the graph of the following (i) y=|(x-1)(x-2)| (ii) |y|=(x-1)(x-2) (iii) y=(|x|-1)(|x|-2) (iv) |(|x|-1)(|x|-2)| (v) |y|=|(|x|-1)(|x|-2)|

The solution of the differential equation, dy/dx=(x-y)^(2) , when y(1)=1, is (A) log_(e) abs((2-y)/(2-x))=2(y-1) (B) -log_(e)abs((1+x-y)/(1-x+y))=x+y-2 (C) log_(e) abs((2-x)/(2-y))=x-y (D) -log_(e) abs((1-x+y)/(1+x-y))=2(x-1)

If x_(1),x_(2) "and" y_(1),y_(2) are the roots of the equations 3x^(2) -18x+9=0 "and" y^(2)-4y+2=0 the value of the determinant |{:(x_(1)x_(2),y_(1)y_(2),1),(x_(1)+x_(2),y_(1)+y_(2),2),(sin(pix_(1)x_(2)),cos (pi//2y_(1)y_(2)),1):}| is

y = e ^ (xx) x tan ^ (- 1) x, showthat (1 + x ^ (2)) y_ (2) -2 (1-x + x ^ (2)) y_ (1) + (1 -x ^ (2)) y = 0

If the ends of a focal chord of the parabola y^(2) = 8x are (x_(1), y_(1)) and (x_(2), y_(2)) , then x_(1)x_(2) + y_(1)y_(2) is equal to

If the foci of the ellipse 9x^(2)+25y^(2)-36x+50y=164 are (x_(1),y_(1)) and (x_(2),y_(2)) then x_(1)+x_(2)+y_(1)-y_(2) =

If y=x+(1)/(x+(1)/(x+(1)/(x+1))), prove that (dy)/(dx)=(y)/(2y-x)