$$\,\,\mathop {Lim}\limits_{x \to \infty } \left( {{{x + \sin x} \over x}} \right)\,\,$$ equal to

A particle moves along a curve whose parametric equations are: $$\,x = {t^3} + 2t,\,y = - 3{e^{ - 2t}}\,\,$$ and $$z=2$$ $$sin$$ $$(5t),$$ where $$x, y$$ and $$z$$ show variations of the distance covered by the particle (in cm) with time $$t $$ (in $$s$$). The magnitude of the acceleration of the particle (in cm/s²) at $$t=0$$ is _______.

The probability density function of evaporation $$E$$ on any day during a year in a watershed is given by $$$f\left( E \right) = \left\{ {\matrix{ {{1 \over 5}} & {0 \le E \le 5\,mm/day} \cr 0 & {otherwise} \cr } } \right.$$$
The probability that $$E$$ lies in between $$2$$ and $$4$$ $$mm/day$$ in the watershed is (in decimal) _______.

A traffic office imposes on an average $$5$$ number of penalties daily on traffic violators. Assume that the number of penalties on different days is independent and follows a Poisson distribution. The probability that there will be less than $$4$$ penalties in a day is ________.