Math 1507

October 8, 1997
Tom Morley
Name: ____________________________

Don't Panic

Open Book and Notes. You have one half hour. Carefully explain your proceedures and answers

Problem 1 (10 Points)

907/40//N

Let ⌊ x ⌋ denote the floor (greatest integer function, denoted in the book as [x]). Graph  ⌊(x^2)⌋ , x and x ⌊(x^2)⌋..   Show that it is differentiable at x = 0 and calculate its derivative. Carefully explain your proceedures and answers.

Problem  2 (10 Points)

Calculate the derivative of f(t) = 3  (t^2)  +  4  using the definitiion of the derivative

Problem 3 (10 Points)

Let f(t) = sin(t). ITOT (It turns out that) f'(t) = cos(t). Do not worry about what these things are. Find the equation of the tangent line to f at the value t = π/3. For your information, 
sin(π/3) =((Sqrt[3])/2) , and cos(π/3) = (1/2). Express the answer exactly.