Test 1
Covers sections 1.1 (Limits), 1.2 (More Limits), 1.3 (Continuity), 1.5 (Derivatives), 1.6 (Simple Rules for Derivatives), 1.7 (Product Rule), 1.8 (Quotient Rule)

To study for test 1:
1) Know everything on this study guide.
2) Study problems from HW1-HW6.
3) Study your GW problems.
4) Try the webwork problems from any of these sections.

Concepts:
1) Know that a limit exists if:
     (i) lim f(x)   = (ii)  lim f(x)
        x->a+               x->a-
2) Know how to find limits on a graph and how to find f(a) on a graph. 
3) If limit = 0/0, factor numerator and denominator, cancel common factors, then take the limit.
4) Know that the limit as x--> +/- infinity of a polynomial is just the limit as x--> +/-infinity of the leading term.  So for a rational function it will be the limit as x--> +/-infinity of the leading term over the leading term after simplifying.
5) Know that a function is continuous at x = a if:
     (i) lim f(x)   = (ii)  lim f(x)   =  (iii) f(a)
        x->a+               x->a-
6) Know how to use the limit definition to find the derivative of a function (one of the given formulas on the test).
7) Know the simple rules for derivatives:
    (i) (const.)' = 0
    (ii) (ax)' = a
    (iii) (xⁿ) = nx^n-1
    (iv) (c f(x))' = c f '(x)
    (v)  (f(x) + g(x))' = f '(x) + g '(x)
8) Know how to use the product rule --> (f g) ' = f ' g + f g '
9) Know how to use the quotient rule --> (f/g) = (f ' g - f g ' )/g²
10) Know how to use all the given formulas on the test: