Find the following limits:
(a) If lim x → 3 ( f ( x ) 2 x + 1 ) = 2 , {\displaystyle \lim _{x\rightarrow 3}{\bigg (}{\frac {f(x)}{2x}}+1{\bigg )}=2,} find lim x → 3 f ( x ) . {\displaystyle \lim _{x\rightarrow 3}f(x).}
(b) Find lim x → 0 tan ( 4 x ) sin ( 6 x ) . {\displaystyle \lim _{x\rightarrow 0}{\frac {\tan(4x)}{\sin(6x)}}.}
(c) Evaluate lim x → ∞ − 2 x 3 − 2 x + 3 3 x 3 + 3 x 2 − 3 . {\displaystyle \lim _{x\rightarrow \infty }{\frac {-2x^{3}-2x+3}{3x^{3}+3x^{2}-3}}.}
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