2.1.73 Calculation of Limits

Condition: Find the limits of functions without using the rule of the Lotal. a) \ (\ lim _ {x \ rightarrow 1} \ frac {\ sqrt {x} -1} {x^{2} -1} \) \ (\ lim _ {x \ rightarrow \ pi}}} \ frac {x^{2}-\ pi^{2}} {\ sin x} \) c) \ (\ lim _ {x \ rightarrow \ infty} \ frac {15 x^{4}-(x+2)^{2}} {(x+1)^{2} -3 x^{4}} \), d) \ (\ lim _ \ rightarrow 0} \ left (\ frac {2+x} {2-x} \ right)^{\ frac {3+x} {x}} \).