If the value of `lim_(x->0)( ((3/ x)+1)/((3/x)-1))^(1/x)` can be expressed in the form of `e^(p/q)`, where p and q are relative prime then find the value of (p+q) .

Let f(x)=(2x-pi)^(3)+2x-cos x .If the value of (d)/(dx)(f^(-1) (x)) at x=pi can be expressed in the form of (p)/(q) ( where p and q are natural numbers in their lowest form), then the value of (p+q) is

Let a,b,c,d are distinct numbers to be chosen from the set {1,2,3,4,5}. If the least possible positive solution for x to the system of equations ax+by=1cx+dy=2} can be expressed in the form (p)/(q) where p and q are relatively prime,then find the value of (p+q).

If 2009 = p^a x q^b where p and q are prime numbers, then the value of (p+q) is

Show that 1.272727=1.27 can be expressed in the form (p)/(q), where p and q are integers and q!=0

If x^(2)-2x-1 is a factor of px^(3)+qx^(2)+1 , (where p , q are integers) then find the value of p +q.

Show that 1. 272727=1. 27 can be expressed in the form p/q , where p and q are integers and q!=0.

If log_(b)a=3,log_(b)=-4. If the value of x satisfying theequation a^(3x)=c^(x)-1 is expressed in the form (p)/(q), where p and q are relatively prime then p+q is

The value of sum_(n=1)^(oo)(1)/((3n-2)(3n+1)) is equal to (p)/(q), where p and q are relatively prime natural numbers.Then the value of (p^(2)+q^(2)) is equal to