BRIEF ANSWERS FOR TEST 1

1. T or F?
   1. F. Width is independent of length.
   2. F. For example, the domain of f(x) = root[2](x-2) is [2,infinity) while the domain of f(2*x) is [1,infinity).
   3. F. Choose any discontinuous function f(x), and let g(x) = -f(x). Then f(x) and g(x) are both discontinuous, but f(x)+g(x) = 0 is continuous.
2. Give the definition.
   1. a = e is the number with the property that the slope of the tangent line to y = log_a(x) is 1 at x = 1.
   2. for every epsilon greater than 0 there exists delta greater than 0 such that [0 less than |x-a| less than delta implies |f(x)-L| less than epsilon]
   3. lim_{x goes to a} f(x) = f(a)
3. Solve the equation.
   1. x = ln(2)
   2. x = 3/4
4. Find the inverse.
   1. y = e^3 - 3
   2. y = (3x+1)/(x-2)
5. Find the limit.
   1. limit = 5/4
   2. limit = -1/(2*root[2](2))
   3. limit does not exist
   4. limit = 1/2
6. Where is f continuous?
   1. continuous everywhere
   2. continuous everywhere except at x = -2
   3. continuous everywhere except at x = 1, -1
   4. continuous everywhere except at x = n*Pi, n an integer