Don't have my book or audio?  You can download a free sample of my book and audio lectures containing Lessons 1 and  2:

Did you read my tips on how to study and learn Math 1500?  If not, here is a link to those important suggestions:

Did you see my tips for Assignment 1? Click here.

Did you see my tips for Assignment 2? Click here.

These are tips for the first assignment in the Distance/Online Math 1500 course, but I strongly recommend that you do this assignment as homework even if you are taking the classroom lecture section of the course.  These assignments are very good (and challenging) practice.  The first assignment is a great way to build and review key skills that will be helpful for this course.

Here is a link to the actual assignment, in case you don't have it:

Study Lesson 5 (The Differentiation Rules), Lesson 6 (Implicit Differentiation), Lesson 7 (Related Rates), and Lesson 8 (Log and Exponential Derivatives)  from my Intro Calculus book to prepare for this assignment.

A good runthrough of your differentiation rules as taught in Lesson 5 and Lesson 8.  Make sure you have studied both of those lessons before you attempt this question.  Very challenging derivatives.  Lots of chain rules involved.

These are very challenging trig limits using the principles I illustrate in Lesson 2, question 16.  Both are a matter of exploiting the sinh/h pattern.

Don't let that polynomial on the bottom scare you.  Just slide it out of the way to make room for what you want down there to match up with sin(7x) up top.  Then, that will create a polynomial limit beside the trig limit that is just a classic 0/0 factor and cancel limit.

Don't let theta confuse you.  That is just a variable, no different than if they used x.  Ignore the question they have given you, and, instead, compute the limit of the reciprocal.  Which is to say, literally, flip the question upside down, and solve that limit instead.  It is kind of similar to my question 16(a) at that point, in that you can separate the problem into two separate fractions.  One cancels nicely and the other fits h/sinh. 

Once you have solved that limit, you can return to the question they gave you.  Their limit must just be the reciprocal of your limit.  Which is to say, if your limit works out to be 3/2 (it won't), then their limit must be 2/3.

You should find my Optional Proofs in Lesson 5 of help here, especially page 158.  Note that k is just a coefficient, so it is merely a matter of multiplying k in to every step of my proof.  Note that k is only part of the top.  Which is to say, k cotx = (k cosx) / sinx.

Classic implicit diff as taught in my Lesson 6.  But also look at the implicit diff examples in Lesson 8.

Very similar to my Lesson 8, question 2.  Note the added bonus that lne = 1.

Classic related rates (Lesson 7) similar to my question 2.  Note that the triangle will be just sides of x, y and z and that the sides are getting smaller, so list your rates as negative values!

Classic related rates (Lesson 7) similar to my Practise Problem 1.  But there is a twist!  They don't want dx/dt or dy/dt.  They want dz/dt where z is the distance between two points formula.  I use that formula in Lesson 10, question 9, page 323.  Ignore the context of that problem as it has nothing to do with related rates, but it does show you how to set this problem up.

In fact, the distance between two points formula is just an application of Pythagorean Theorem.  Here, because the second point is just the origin (0,0) and the point of interest is any point on the curve (x,y), this amounts to z being the hypotenuse of a right triangle with horizontal leg x and vertical leg y.

Make a rough sketch of the given graph (I would use the points where x = 0, 1/2 and 1 and keep in mind that this is just a sine curve.  Draw a diagonal line from the origin to a random point on the curve in the first quadrant which you have labelled with coordinates (x, y).  That diagonal line is z the distance between the origin and the curve.  It is also the hypotenuse of a right triangle with horizontal leg x and vertical leg y.  You are given dx/dt, but you also need to know dy/dt.  I would compute that first, by doing the derivative of the given equation for y.  You are now ready to exploit the Pythagorean Theorem to compute dz/dt.