2.1.40 Calculation of Limits

Condition: using the 2nd remarkable limit, calculate the limits: a) \ (\ lim _ {x \ rightarrow \ infty} \ left (\ frac {x+3} {x-2} \ right)^{2 x+1} \), b) \ (\ lim _ {x _ {X \ Rightarrow \ Infty} \ Left (1+ \ Tan ^{2} \ SQRT {X} \ RIGHT) ^{3} {X} ELD \), B) \ (LIM {X \ RIGHTARROROUN \ InFTY} x (\ ln (2+x)-\ ln x) \), d) \ (\ lim _ {x \ rightarrow 0} \ frac {1} {x} \ ln \ sqrt {\ frac {1+x} {1-x}} \).