" Q."(x+(1)/(x))^(x)+x^((1+(1)/(x)))

If x is nearly equal to 1 show that (a) (px^(p)-qx^(q))/(p-q)=x^(p+q) (nearly) (b) (px^(q)-qx^(p))/(x^(q)-x^(p)) =(1)/(1-x) (nearly) (Hint : Take x=1+delta x and proceed)

int((x^2+1))/((x+1)^2)dxi se q u a lto ((x-1)/(x+1))e^x+c (b) e^x((x+1)/(x-1))+c e^x(x+1)(x-1)+c (d) none of these

If y = (1)/(1+x^( p-r) +x^(q-r)) +(1)/( 1+ x^(p-q) +x^(r-q) )+ (1) /( 1+x^(q-p) +x^(r-p)),then (dy)/(dx) =

(d)/(dx) [(x +1)(x^2+1)(x ^(4) + 1) (x ^(8) +1)]=(15 x ^(p) -16x^q+1) (x-1) ^(-2) implies (p,q)=

Simplify (i) ((x^(i))/(x^(m)))^((1)/(lm)).((x^(m))/(x^(n)))^((1)/(m)).((x^(n))/(x^(l)))^((1)/(nl)) (ii) ((x^(p))/(x^(q)))^((1)/(ml)).((x^(q))/(x^(r)))^((1)/(mn)).((x^(r))/(x^(p)))^(r+q)

find the value of x:(1)/(x+p+q)=(1)/(x)+(1)/(p)+(1)/(q)

(((1)/(x)+y)^((a+b))((1)/(y)-x)^(-(p+q)))/(((1)/(x)-y)^(-(p+q))(x+(1)/(y))^((a+b)))=

Evaluate : ((x^(q))/(x^(r )))^((1)/(qr))xx((x^(r ))/(x^(p)))^((1)/(rp))xx((x^(p))/(x^(q)))^((1)/(pq))