2.1.30 Calculation of Limits

\ (\ underline {\ text {Condition:}} \) Find the limits: A) \ (\ LIM _ {X \ RIGHTARROW 0} \ FRAC {\ TAN \ PI X+2} {X^{2} +2 X-3} EL) \ (\ LIM _ {X \ Rightarrow 3} \ FRAC {\ SIN ^{2} \ FRAC {\ Pi X} {3}} {X ^} -4} E) \ (\ LIM _ {X \ RIGHTARROUN+\ InFTY} \ frac {16-x^{4}} {x^{4} -2 x+3} \), d) \ (\ lim _ {x \ rightarrow-1} \ frac {5 x^{2} +3 x-2} {x^{2} -1} \).