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=== 01 === wk. 36

* All problems are taken from the exam problem collection, except the last which is just quoted below:


* You will need:
 - recall the definition of inflection point, which is where f'' changes sign.
 - the 'range' ('verdimengden') of a function f = those values that f attains when x runs through the entire domain of definition
Notice that 'sketch' a graph means 'sketch' -- get the qualitative properties visible, not get it pretty. Don't spend too much time on this.


* Problems:
 - From the compendium: 15, 18, 32  except part (c), 115, 117.
 - Let F(x,y) = x exp(y) be a production function defined for nonnegative x,y. Consider a level curve F(x,y)=C, C>0, on which y is a function of x.
   Then y can be solved explicitely as y= ln C - ln x, but in problems (a)--(c) you are asked to NOT solve this way, but use the implicit calculations rules:
      (a) Compute the MRS = - dy/dx on this level curve using implicit differentiation.
      (b) Compute the elasticity of y wrt. x
      (c) Compute the elasticity of substitution of F by using the fomula in the book
      (d) Verify your answers in (a)--(c) by calculating in a different manner (in (a), (b) use the form y = ln C - ln x, while in (c) calculate the ratio d ln (y/x) / d ln MRS.





=== 02 === wk. 37 ===

From the compendium: problems
43 
44 
53 (c) 
54 
110 (a)





=== 03 === wk. 38 ===

Problem 30 from the compendium.
Then, replace the equality sign in the constraint by ¡Ü (less-than-or-equal), consider merely the maximization problem, and use your calculations from the Lagrange problem to check which points satisfy the Kuhn--Tucker conditions.

Problem 132 from the compendium
Exam autumn 2007 problem 2
Exam autumn 2007 problem 4
Exam autumn 2009 problem 2





=== 04 === wk. 39 ===

Some of these problems involve integrals that are not easy without practice; you could try a few easier ones from the book first.  And if you are still stuck, try again after Monday's lecture.  All problems from the compendium:

Problem 28 (this is a long one, from the era of full-day exams. Don't worry if you find it hard.)
Problem 21 (a)
Problem 49
Problem 100 (a), (b) -- for the latter there are many choices where you would have to substitute again.
Problem 109 (a)
Problem 110





=== 05 === wk. 40 ===

All from the collection:

88
94
100
120 -> this is solvable both as a separable and as a linear differential equation. Do both (the latter requires Monday's lecture).
127 -> solve part (a) in two different ways.
134 -> part (a) requires Monday's lecture.

And if this joke helps you remember the constant, then it's worth it:
- What is the indefinite integral of 1/cabin wrt. cabin?
- ... a log cabin? 
- No, a houseboat. You forgot the C.



=== No teaching wk 41
=== 06 === wk. 42 ===

Problem 53 (a) and (b) 
Problem 65 (a)
Problem 71
Problem 84
Problem 109 

Exam spring 2009 # 4