**6.** Find the arc length for the spiral whose polar equation is over the interval .

The “key example”: the *easiest* problem of its type. Should this be on a final exam? Heck no, it should be assigned early on and then referred to often. Here it is now. The old “unchanged by differentiation” trick…

**5.** Find a formula for the slope of the tangent to the “epicycloid” whose parametric equations are and .

Routine; I passed over it in near-silence on the review day. Also… owen by the way… played ‘em ILMB and For John Henry.

**4.**Recall that the Taylor Series for the exponential function is . Use the Taylor polynomial to obtain a (rational number) estimate for (write out the first four terms of the series; put ; simplify). Find a reasonable upper bound on the “error term” for this estimate.

The class that had this final didn’t “get” the control-the-error parts of the course; this one I didn’t even really try. *You* should… whoever you are… but if you’re my student, I’ll go ahead and admit there won’t be an “error term” problem on *this* quarter’s exam. Be able to write out a Taylor Series and use it in estimating a number; the rest, for us, is gravy.

More still to come I imagine.

### Like this:

Like Loading...

*Related*

November 2, 2009 at 7:52 am

Maths too hard for me when i was in school and college i used to get low marks in maths the formulas it have o my god.