consider `f(x)==cos^-1x+xos((sqrt3 x+sqrt(1-x^2))/2)`, if `sum_(r=1)^100 f(1-(1/10)^r)=p/q pi` where `p` and `q` relatively prome number then find the value of `p-16q`

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)|

Let d bet the minimum value of f(x)=5x^(2)-2x+(26)/(5) and f(x) is symmetric about x=r. If sum_(n=1)^(n=1)(1+(n-1)d)r^(n-1) equals,(p)/(q), where p and q are relative prime,then find the value of (3q-p).

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)

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

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) .

If f(x) = px +q, where p and q are integers f (-1) = 1 and f (2) = 13, then p and q are

sqrt(x^(p-q))sqrt(x^(q-r))sqrt(x^(r-p))=1

If p inR and q = log_(x) (p+sqrt(p^(2)+1)) , then find the value of p in terms of x and q.