Prove that the function `f(x)= x^(n)` is continuous at x= n, where n is a positive integer.

Prove that the function f(x) = 5x - 3 is continuous at x = 0, at x = -3 and at x = 5.

Prove that the function defined by f(x)= tan x is a continuous function.

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

Prove that 2^(n) gt n for all positive integers n.

If f(x) = (a-x^n)^1/n, a gt 0 , n is a postive integer then f[f(x)]=

The sum of the coefficients in the expansion of (6 x-5 y)^(n) where n is a positive integer, is

If a and b are distinct integers, prove that a-b is a factor of a^n - b^n , whenever n is a positive integer.

Is the function defined by f(x)= |x| , a continuous function?

Show that one and only one out of n, n + 2 or n + 4 is divisible by 3, where n is any positive integer.