`(x-2)/(x^2+1)<(-1/2)`

Show that Lt_(x rarr2^(-))(|x-2|)/(x-2)=-1

int((1-x^(-2))/(x^(1/2)-x^(-1/2))-(2)/(x^(3/2))+(x^(-2)-x)/(x^(1/2)-x^(-1/2)))dx

int((1-x^(- 2))/(x^(1//2)-x^(-1//2))-2/(x^(3//2))+(x^(- 2)-x)/(x^(1//2)-x^(-1//2)))dx

tan((1)/(2) sin ^(-1)""(2x)/(1+x^(2))+(1)/(2)cos^(-1)((1-x^(2))/(1+x^(2))))=(2x)/(1-x^(2))(|x|ne 1)

To prove that tan((1)/(2)sin^(-1)((2x)/(1+x^(2)))+(1)/(2)cos^(-1)((1-x^(2))/(1+x^(2)))=(2x)/(1-x^(2))

(x^(2))/((x+1)^(2))+((x+1)^(2))/(x^(2))-(x)/(x+1)+(x+1)/(x)-(7)/(4)=p^(2)

if y=x^2+1/(x^2+1/(x^2+1/(x^2+...............oo))) then (dy)/(dx)

Using the properties of determinants, prove the following |{:((x-2)^2,(x-1)^2,x^2),((x-1)^2,x^2,(x+1)^2),(x^2,(x+1)^2,(x+2)^2):}|=-8