lab7.mws Lab Overview Example 1: Limit( arctan(3*x)/arcsin(x), x=0 ) (p. 407, # 4) Example 2: Limit( x*ln(x), x=0, right ) Example 3: Limit( a^(1/n), n=infinity ) ( a > 0) Example 4: limit( (1+x)^(1/x), x=0, right ) Example 5: Limit(x^(5/2)*exp(-x/30),x = infinity); Note: Essay Question Initial Analysis First Application of l'Hopital's Rule Second Application of l'Hopital's Rule Third Application of l'Hopital's Rule Final Analysis Example 6: p. 413, # 48 Note: Count Your Blessings! (a) (b) (c) (d) Concluding Remarks Observation 1: Limit( f[n](x), x=infinity ) and Limit( f[n](x), n=infinity ) are very different questions Observation 2: Interchanging limits is not always permitted Lab Questions