$$\mathop {\lim }\limits_{x \to 0} \,\,{{{{\left( {27 + x} \right)}^{{1 \over 3}}} - 3} \over {9 - {{\left( {27 + x} \right)}^{{2 \over 3}}}}}$$ equals.

Let $${1 \over {{x_1}}},{1 \over {{x_2}}},...,{1 \over {{x_n}}}\,\,$$ (x_i $$ \ne $$ 0 for i = 1, 2, ..., n) be in A.P. such that x₁=4 and x₂₁ = 20. If n is the least positive integer for which $${x_n} > 50,$$ then $$\sum\limits_{i = 1}^n {\left( {{1 \over {{x_i}}}} \right)} $$ is equal to :

Let M and m be respectively the absolute maximum and the absolute minimum values of the function, f(x) = 2x³ $$-$$ 9x² + 12x + 5 in the interval [0, 3]. Then M $$-$$m is equal to :

If the function f defined as

$$f\left( x \right) = {1 \over x} - {{k - 1} \over {{e^{2x}} - 1}},x \ne 0,$$ is continuous at

x = 0, then the ordered pair (k, f(0)) is equal to :