Find n if `underset(xrarr2)Lt(x^n-2^n)/(x-2)` = 12, n being a positive integer.

If lim_(x rarr 2) (x^n-2^n)/(x-2)=80 and if n is a positive integer, find n.

underset(xrarra)lim (x^n-a^n)/(x-a) is equal to:

underset(xrarr2)lim (x^3-x^2+1) is equal to:

Verify Rolle's Theorem in the interval [a,b] for the fraction: f(x) = (x-a)^m(x-b)^n,m and n being positive integers. Find the value of 'c'.

Evaluate: underset(xrarr2)lim (x^3-4x^2+4x)/(x^2-4) .

Prove that (n!)^2 le n^n. (n!)<(2n)! for all positive integers n.

Show that the middle term in the expansion of (1+x)^(2n) is (1.3.5….(2n-1))/(n!) 2^(n)x^(n) , where n is a positive integer.

Using Permutation or otherwise, prove that ((n^2)!)/((n!)^2) is an integer, where n is a positive integer.

Write the middle term in the expansion of : (1+x)^(2n) , where n is a positive integer.