If `agt0, b gt0` than `underset(nrarroo)(lim)((a-1+b^((1)/(n)))/(a))^(n)=`

If agt0, b gt0 than lim_(nrarroo) ((a-1+b^((1)/(n)))/(a))^(n)=

underset(xrarr0)lim((1)/(sin x)-(1)/(x))

lim_(nrarroo) (3.2^(n+1)-4.5^(n+1))/(5.2^(n)+7.5^(n))=

The value of lim_(nrarroo) ((n^(2)-n+1)/(n^(2)-n-1))^(n(n-1) is

At the point P(a,a^(n)) on the graph of y=x^(n)(n in N) in the first quadrant at normal is drawn. The normal intersects the Y-axis at the point (0, b). If underset(ararr0)(lim)b=(1)/(2) , then n equals ……………

If a + b =1, a gt 0,b gt 0, prove that (a + (1)/(a))^(2) + (b + (1)/(b))^(2) ge (25)/(2)

Find the value underset(n rarr oo)("lim") underset(k =2)overset(n)sum cos^(-1) ((1 + sqrt((k -1) k(k + 1) (k + 2)))/(k(k + 1)))

Evaluate underset(theta rarr 0)(lim) (1- cos m theta)/(1- cos n theta)

If ab=2a+3b, agt0, b gt0 , then the minimum value of ab is

Prove that lim_(xrarr0) ((1+x)^(n) - 1)/(x) = n .