A little time spent now reviewing algebra and calculus
facts will save you a lot of time
later. So pull your calculus textbook off the bookshelf and do the fol lowing
questions .
(1) Suppose 
. True or false ( circle one ): is
y = x-1 + C-1?
(If you're not sure, then try it with actual values for x and C .)
If false, then find a correct formula for y :
(2) Notation: in mathematics "log" means the same thing as "ln", in other words
the
natural logarithm or logarithm to base e.
Suppose ey = x + 1. True or false (circle one): is y = log x + log 1? If false,
then
find a correct formula for y:
(3) Suppose arcsin y = x + π/6. True or false (circle one): is y = sin(x) +
sin(π/6)? If
false, then find a correct formula for y:
(4) A quadratic equation 
can be solved by factoring the
equation as
in which case the roots are 
and
, or else by invoking the quadratic
formula
Advice. Since it is often difficult to see how to factor a quadratic equation,
your best
bet is usually to invoke the quadratic formula.
Here are the questions: find the roots of
(i) 2x2 - 4x - 7 = 0
(ii) 2x2 - 4x + 7 = 0
(5) Consider a graph y = f(x). Using that
equals the slope of the graph at
the point (x, f(x)) on the graph, explain with a picture why it is that
,
where Δy = f(x + h) - f(x) and Δx = (x + h) - x = h, and h is small.
[Recall 
is called a difference quotient , and gives the "rise in y" divided by the
"run in x". The difference quotient justifies our inter pretation of the
derivative 
as
a rate of change of quantity y with respect to changes in quantity x.]
(6) Evaluate the following derivatives, and antiderivatives (indefinite
integrals):
