Exercises

1. 1. Use Maple to compute the following integral:

      

   2. Use Maple to differentiate

      

      and ``simplify'' the result. You got back f(x), although g is different from the answer you got in a. Explain why.

2. Use Maple to determine if the following pairs of functions are inverses. Be sure that you justify your answer using the definition of inverse function.
   1. 
   2. 
3. Use Maple to solve for x in the equations:

   

   Are all the solutions acceptable? Use a monotonicity argument to show that the above equations cannot have more than one solution.

4. Use Maple to determine the inverse of the function defined, for any real x, by:

   

   Once you have determined the inverse, plot the function, its inverse and the line y=x on the same graph.