Problem 1. Find the following limits: (a) lim x → 0 tan ( 3 x ) x 3 . {\displaystyle \lim _{x\rightarrow 0}{\frac {\tan(3x)}{x^{3}}}.} (b) lim x → − ∞ x 6 + 6 x 2 + 2 x 3 + x − 1 . {\displaystyle \lim _{x\rightarrow -\infty }{\frac {\sqrt {x^{6}+6x^{2}+2}}{x^{3}+x-1}}.} (c) lim x → 3 x − 3 x + 1 − 2 . {\displaystyle \lim _{x\rightarrow 3}{\frac {x-3}{{\sqrt {x+1}}-2}}.} (d) lim x → 3 x − 1 x + 1 − 1 . {\displaystyle \lim _{x\rightarrow 3}{\frac {x-1}{{\sqrt {x+1}}-1}}.} (e) lim x → ∞ 5 x 2 − 2 x + 3 1 − 3 x 2 . {\displaystyle \lim _{x\rightarrow \infty }{\frac {5x^{2}-2x+3}{1-3x^{2}}}.}
