Evaluate :
`lim_( p -> 0 ) ( Sinp/p )^2`

Evaluate: lim_(n rarr oo)(n^(p)sin^(2)(n!))/(n+1)

Evaluate: (lim)_(x->0)sin8xcot3x . If it is of the form p/q , then (p+q)= ?

Evaluate lim_(ntooo) (n^(p)sin^(2)(n!))/(n+1),"wher "0ltplt1.

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) .

Leg p_(n)=a^(P_(n-1))-1,AA n=2,3,..., and let P_(1)=a^(x)-1 where a in R^(+). Then evaluate lim_(x rarr0)(P_(n))/(x)

Find the value of p(p gt 0) if (15)/(4) + p, (5)/(2) + 2p and 2+ p are the three consecutive terms of a geometric progression.

Evaluate the following (i) lim_(n to oo)((1)/(n^(2))+(2)/(n^(2))+(3)/(n^(2))....+(n-1)/(n^(2))) (ii) lim_(n to oo)((1)/(n+1)+(1)/(n+2)+....+(1)/(2n)) (iii) lim_(n to oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+....+(n)/(2n^(2))) (iv) lim_(n to oo)((1^(p)+2^(p)+.....+n^(p)))/(n^(p+1)),pgt0

3.The value of lim_(x rarr0)(p^(x)-q^(x))/(r^(x)-s^(x)) is

Find the value of sum_(p=1)^(n)(sum_(m=p)^(n)C_(m)^(m)C_(p)) And hence,find the value of lim_(n rarr oo)(1)/(3^(n))sum_(p=1)^(n)(sum_(m=p)^(n)C_(m)^(m)C_(p))