If `lim_(x->0) ((tan(pi/4+x))^(1/x)-e^2)/x^2` is equal to `(p/q)e^2`, (`pqepsilon N`) , then find minimum value of(p+q)

If lim_(x->1)((x^n-1)/(n(x-1)))^(1/(x-1))=e^p , then p is equal to

Let p=lim_(x->0^+)(1+tan^2 sqrt(x))^(1/(2x)) then log p is equal to

lim_(x->0)sin^2(pi/(2-p x))^(sec^2((pi/(2-q x)))

lim_(xtooo) (e^(1//x^(2))-1)/(2tan^(-1)(x^(2))-pi) is equal to

lim_(xtooo) (e^(1//x^(2))-1)/(2tan^(-1)(x^(2))-pi) is equal to

lim_(xtooo) (e^(1//x^(2))-1)/(2tan^(-1)(x^(2))-pi) is equal to

P=x^3-1/x^3, Q=x-1/x x in (1,oo) then minimum value of P/(sqrt(3)Q^2)

If sum of all the solutions of the equation (4tan x+tan^(2)x+1)=2sqrt(2)sin(x+(pi)/(4))(1+tan^(2)x) in [0,pi] is (p, (pi)/(q)) where p,q are relatively prime number, then find the value of (p+q)

If lim_(x rarr0)(x+ln(sqrt(x^(2)+1)-x))/(x^(3))=(p)/(q) where p and q are coprimes then find the value of |p^(2)-q^(2)|