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?

Did you see my tips for Assignment 2?

These are tips for the assignments 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.

For f(x), try dividing every term, top and bottom by "sinx" first. Then, the limit is trivial if you remember Lesson 2, question 16.

I have no idea how they expect you to solve the limit for g(x) without knowledge of L'Hopital's Rule. Has there been a change in the course? You can't be using L'Hopital's Rule since that requires derivatives, and you are just starting doing derivatives.

My only guess is that you have been given the definition for Euler's Constant, e.  Look at the wikipedia entry about this, and the formula given in the History section especially

Unless they have given you an awfully similar example in your course notes (take a look and let me know), I can only assume this is put here to intentionally make you all suffer.

Look at the graph they are referring to and visualize what the tangent lines look like at several points in each question. Remember, f' is the slope of the tangent line. As you read the graph left to right, is the tangent line rising (positive slope), falling (negative slope), or horizontal (slope of 0)? First, find all the points where the tangent line is horizontal, telling you f' = 0, and then you can plot 0 on the f' graph for each of those x-values. Then, determine if the graph of f' in each section is dipping below 0 or above 0 based on whether the slope of f is negative or positive.

Make sure you have thoroughly studied both Lessons 5 and Lesson 8 before attempting these derivatives. I warn you! You must have learned Lesson 8, too, before you start this question. Otherwise, you are just not ready to properly see the method required to solve each question.

Apparently, they are expecting you to also know the derivatives of the inverse trig functions. Note that I teach these in Lesson 1 of my Calculus 2 book, question 2. That lesson is available to download for free on my website:

Free sample of my Calculus 2 book and accompanying audio.

Study Lesson 6 to learn implicit differentiation before attempting this question. Also, look at the additional examples of implicit diff that I do in Lesson 8.

Similar to the proof of sinx that I discuss in Lesson 5.

Using the position-velocity-acceleration, h-h'-h" connection that I discuss in Lesson 5, question 5.

Maximum height occurs at the moment when velocity is 0. Compute the derivative, h', to get a formula for the velocity, v, and then set v equal to 0 to solve the time, t.

The volume of water in this trough would be the area of the triangle times the length.The length is constant (20 metres), but the base, b, and the height, h, are changing at all times as the water rises. You will need to use Pythagorean Theorem to find the constant height of the actual trough, keeping in mind that all three sides of the equilateral triangle are constant at 10 metres each. You can then use similar triangles to eliminate b from the water volume equation. Your Volume formula should have strictly h as a variable before you compute the derivatives.

Note that, if y = inverse secant (x^2), then x^2 = sec(y). Now, find dy/dx using implicit diff.

Note, that your answer for dy/dx will have secy tany in it (if you have done it right). You must then get rid of secy and tany. Of course, you know that secy is x^2. You can use the idenity that tan^2 + 1 = sec^2 to figure out what tany must be in terms of x.