What is the limit as approaches infinity of ?
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Use analytical methods to evaluate the following limits.
1) limit as x approaches infinity of x^2ln(cos(1/x))
2) limit as x approaches pi/2 of (pi-2x)tanx
3) limit as x approaches 0+ of x^(1/lnx)
4) limit as n approaches infinity of (1+2+...+n)/n^2
5) Suppose a and b are real numbers. Evaluate the limit as x approaches infinity of (ax-sqrt(a^2x^2-bx))