by AuSmith » Wed Apr 11, 2007 7:02 pm
Actually, do we ever have to use Taylor series? All Maclaurin is is a Taylor with center at x=0. In a Taylor series with center of convergence at a, you have (x-a) sprout up everywhere.
22) Yea, I don't like this one. The pattern looks unclear. First, I looked for a series to fit... maybe one with Bernoulli numbers. Didn't work. Next, I hoped maybe since [unparseable or potentially dangerous latex formula], that it was just a maclaurin with fractions in lowest terms. Then, I tried fitting x=2/3... hrm
23) I get 11.6
59) Say [unparseable or potentially dangerous latex formula]. Take away the 3 squares and middle triangle. Now, move two of the remaining triangles along the bold lines. It makes a single triangle. The squares of the sides of this triangle are [unparseable or potentially dangerous latex formula]... No, nevermind. Try again. Look at any one of the angles of the center triangle. The opposite angle is supplementary (sum of the 4 is 360, minus the two right angles), and has the same sine. It also has the same two adjacent legs. Therefore, the areas of the 4 triangles are the same.