I had a piece of carpet leftover from our living room installation. There is a pass thru that is in high traffic area and I thought it would be nice to use a matching piece but I didn't want to spend a lot of money as I expect it to get dirty quickly and need replacing. I thought that this would be worth a try.
Section 1.4, Limits involving inï¬nity p. 45 (1/3/08) The trigonometric functions do not have limits as x â Â±â because they are periodic. The inverse. sine and cosine functions do not have limits as x â Â±â because they are deï¬ned only for â1 â¤ x â¤ 1. The.
Note that we really do need to do the right-hand limit here. We know that the natural logarithm is only defined for positive x and so this is the only limit that makes any sense. Now, in the limit, we get the indeterminate form . LâHospitalâs Rule wonât work on products, it only works on quotients. However, we can turn this into a fraction if we rewrite things a little. The function is the same, just rewritten, and the limit is now in the form and we can now use LâHospitalâs Rule. Now, this is a mess, but it cleans up nicely.