The range of values of $$k$$ for which the function $$\,\,f\left( x \right) = \left( {{k^2} - 4} \right){x^2} + 6{x^3} + 8{x^4}$$ has a local maxima at point $$x=0$$ is

$$\mathop {\lim }\limits_{x \to 0} \left( {{{{e^{5x}} - 1} \over x}} \right)$$ is equal to ________.

A fair coin is tossed $$N$$ times. The probability that head does not turn up in any of the tosses is

A normal random variable $$X$$ has the following probability density function $$${f_x}\left( x \right) = {1 \over {\sqrt {8\pi } }}e{}^{ - \left\{ {{{{{\left( {x - 1} \right)}^2}} \over 8}} \right\}}, - \infty < x < \infty $$$
Then $$\,\int\limits_1^\infty {{f_x}\left( x \right)dx = } $$