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ALGEBRA, CALCULUS REVIEW

A little time spent now reviewing algebra and calculus facts will save you a lot of time
later. So pull your calculus textbook o the bookshelf and do the following questions.

(1) Suppose 1/y = x + C. True or false ( circle one ): is

(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 ar^2 + br + c = 0 can be solved by factoring the equation as

in which case the roots are r = r1 and r = r2, 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

(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 , 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 interpretation 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):

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