The most common mistakes on quiz 1

• the limit of (ln x)/x is not (ln x) times 0 or infinity times 0 !!!!!
• stating that (ln x)^2 = 2(ln x). do not confuse (ln x)^2 with ln(x^2) !!!!

part (b):

• one to the infinity power is not 1 !!!!!
• the limit of (1+2/x)^x is not 1^x !!!!!

part (c):

• not recognizing a geometric series
• thinking it was a p-series
• confusing "evaluate" with "does it converge?"
• ... and therefore using the integral test
• ... and writing down the value of the integral as the value of the sum.

part (d):

• not recognizing an alternating series.
• recognizing it but not saying so.
• using the alternating series test but not saying so. (you must say: "by the alternating series test..." or "since this is an alternating series..." or something like that.)

part (a) and (b) both:

• general confusion about indeterminate forms. warning: if you do not know how to recognize an indeterminate form or take its limit, you can expect to do badly on the rest of the course. learn it now!

part (c) and (d) both:

• confusing a limit with a sum, and a sequence with a series.
• using a convergence test for sequences instead of a convergence test for series.