part 2

2. f(x) = int(x)
7. Adjacent over opposite.
8. lim x→c f(x)g(x) = lim x→c f'(x)g'(x).
11. f(x) = x³
12. d/dx [f(x)g(x)] = g(x)f'(x) - f(x)g'(x)[g(x)]2 (A differentiation rule).
14. f’(x) = lim 𝚫x→0 f(x + 𝚫x) - f(x)𝚫x.
21. A theorem that states that if f is continuous on the closed interval [a,b], differentiable on the open interval (a,b), and f(a) = f(b), then there is at least on enumber c in (a,b) such that f’(c) = 0.
22. f(x) = |x|
24. V = 𝝅ab[R(x)]2dx OR V = 𝝅ab[R(y)]2dy.
27. Inverse tangent.
31. Inverse cotangent.
33. The value(s) of x of a function where y = 0.
34. f(x) = 1/(1+e^-x)
35. Inverse cosine.
37. A theorem that states that a continuous function on a closed interval must have a maximum and a minimum and that these extrema can occur at the endpoints.
39. The value of y of a function where x = 0.
41. f(x) = x²
43. y’ = k(y-y0).
44. f(x) = sin(x)
46. A horizontal line that a function approaches, but never reaches.
47. d/dx [cf(x)] = cf’(x) (A differentiation rule).
48. The property of a graph that is either odd, even, or nonexistent.

1. f(x) = x^½
3. f(x) = 1/x
4. The total interval of x where the function exists.
5. d/dx [f(x)g(x)] = g(x)f’(x) + f(x)g’(x) OR f(x)g’(x) + g(x)f’(x) (A differentiation rule).
6. Inverse sine.
9. Opposite over hypotenuse.
10. d/dx = [f(g(x))] = f’(g(x))g’(x) (A differentiation rule).
13. d/dx [f(x) ∓ g(x)] = f’(x) ∓ g’(x) (A differentiation rule).
15. 00 or ∞∞ This does not guarantee that a limit exists, nor does it indicate what the limit is if one does exist.
16. Opposite over adjacent.
17. An existence theorem that states that if f is continuous on the closed interval [a,b] and k is any number between f(a) and f(b), then there is at least one number c in [a,b] such that f(c) = k.
18. f(x) = cos(x)
19. d/dx [c] = 0 (A differentiation rule).
20. A vertical line that a function approaches, but never reaches.
23. Hypotenuse over opposite.
25. f(x) = x
26. f(x) = ln(x)
28. Adjacent over hypotenuse.
29. The total interval of y where the function exists.
30. Inverse secant.
32. f(x) = e^x
36. A theorem that states that if f is continuous on the closed interval [a,b] and differentiabl on the open interval (a,b), then f’(c) = f(b) - f(a)b - a
38. Inverse cosecant.
40. d/dx [x^c] = nx^(n-1) (A differentiation rule).
42. V = 𝝅ab([R(x)]2-[r(x)]2)dx OR V = 𝝅ab([R(y)]2-[r(y)]2)dy.
45. Hypotenuse over adjacent.