Math 191: Supplement on Trigonometric Functions
With reference to the triangle
recall the basic trigonometric ratios sine, cosine and tangent for angles of less than 90 :
Math19lSecF0501-Qui25 um; SOLMTIONS
(1) [5 points] For the following functions nd . the derivative at t = 1:
011 +4. (+.'u (L) '7' L i
- ?+ - 2
dt : (t+q)'l. ( 1 ) (1)
i . 0:- _ s" _ 7-,
: .L . 3.
V + 5 r
Oct 28 2005 Name: 501.1411 Cu 5
(a)[8 points] Use the to nd f(x) where
f(1:) = V23: +1
Im = m
= I m W - 57:?
= Um air-m) 12:1 7m _ J1(1+k)v| 4.1%:
ko k J2(V¢H)N "Jlx-tt'
= ("M 1(x-rk)-H-(Jx-H)
k JDUHJ-H +
Math 191 Sec F0501/F0502
Practice Problems for Test 3
1. Over what intervals is f (x) = x2 ln x increasing? (Begin by determining the domain of f (x).
ans: (e1/2 , )
2. Let f (x) = e 2+g(x) where g(x) is a function with g(6) = 7 and g (6) = 12. Find f (6)
Math 191 Quiz 4 ~ Name: 50 L UtTLON
(1)  Determine the marginal cost when q = 50 units if average cost is given by
State units with your answer.
= anigf-efgy + 3730'
of}; 1: 04218,? g-
M/ aw = owlcmyeft/(D %wr+
Oct 17 2012
p.10f2 Math 191 _ Quiz
Supplement: Trigonometric Functions II
Related Rates Problems
In class we looked at an example of a type of problem belonging to the class of Related Rates
Problems: problems in which the rate of change (that is, the derivative) of an unknown fun
Supplement: Linear Approximation
By now we have seen many examples in which we determined the tangent line to the graph of a
function f (x) at a point x = a. A linear approximation (or tangent line approximation)