2.1.67 Calculation of Limits

Condition: Calculate the indicated limits without using the rule of the Lotal: A) \ (\ LIM _ {X \ RIGHTARROW \ InFty} \ FRAC {3 x^{3} -x+2} {3 x^{2} -2 x^{3} +1 \) \ (\ lim {x {x {x \ Rightarrow 3} \ Frac {x^{2} -9} {6 x^{2} -16 x-6} \) c) \ (\ lim _ \ Rightarrow 0} \ frac {\ sqrt {x+2}-\ sqrt {2}} {\ sqrt {x+3}-\ sqrt {3}} \), d) \ (\ lim _ \ rightarrow 0} \ frac {1- / cos 2 x} {3 x} {3 x} {3 x} {3 x} {3 x x \ cdot \ sin x} \) d) \ \ (\ lim _ {x \ rightarrow+\ infty} x (\ ln (2 x-1)-\ ln (2 x-3) \).