`L_(x->1)[(x-1)/(x^2-x)-1/(x^3-3x^2+x)]`

lim_(x rarr1)[(x-1)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+x)]

im_(-)>1[(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]

lim_(xrarr1) [(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]

lim_(xrarr1) [(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]

lim_(x rarr2)[(x-2)/(x^(2)-4)-(1)/(x^(3)-3x^(2)+x)]=(1)/(m) where l and m are mutually prime then the value of (l+m)

Long-answer type questions (L.A.) (1)/((x-1)(x-2))+(1)/((x-2)(x-3))+(1)/((x-3)(x-4))=(1)/(6)(xne1,2,3,4)

lim_(x rarr1)[((4)/(x^(2)-x^(-1))-(1-3x+x^(2))/(1-x^(3)))^(-1)+3(x^(4)-1)/(x^(3)-x^(-1))]

Let L_(1)=lim_(x rarr0)((sin(2x)+cos(x)-1)/(x)) , L_(2)=lim_(x rarr oo)(sqrt(x^(2)-x)-x) , and L_(3)=lim_(x rarr4)(x^(2)-3x)/(x^(2)-x) , then the value of L_(1)L_(2)+(1)/(L_(3)) is

If D(x)=det[[(x-1),(x-1)^(2),x^(3)(x-1),x^(2),(x+1)^(3)x,(x+1)^(2),(x+1)^(3) then the coefficient of x in D(x), is ]]

If x^(2)+3x+1=0 then find x^(3)+(1)/(x^(3)),x^(4)+(1)/(x^(4)),x^(2)-(1)/(x^(2)),x^(2)+(1)/(x^(2))