1 Darts! Due Thursday 2-3-2011 | 2. Euler and Trig.Due: Thursday, Feb. 10 | 3. A review trip. Due:Thursday, Feb 24 |
4 Some Integrals Due: March 23 |
5. MacLaurin Polynomials and DE's.
Due: April 7 |
6. Comparing functions and polynomials.Due May 2 |
7.Probability and More integration. Due: | 8.A Very Flat Function Due: | Due: | Derivatives and Chemistry Due: |
Estimating
integrals Due: |
Fitting Curves Due: |
The tangent function satisfies the differential equation y'
=
1+y ^{2} with y(0)=0. This allows us to
estimate
the tangent function with Euler's method as the solution to this
differential
equation.
(a) S(x). (b) S'(x).
In your graphs show and explain such features as extrema, concavity, symmetry, etc.
1. Suppose f is a function with f (0) = 0, f (1) = 1, and f
(2)
= 0 .
A Find a trigonometric function trig(x) so that trig(0) = f (0)
= 0, trig(1) = f (1) = 1, and trig(2) = f (2) = 0.
Graph the function trig and find .
B. Find a quadratic polynomial function q(x) so that q(0) = f (0) =
0, q(1) = f (1) = 1, and q(2) = f (2) = 0.
Graph the function q and find
.
2. Suppose f is a function with f (0) = 1, f '(0) = 1, and f
''(0) = -1 .
A. Find a trigonometric function rig(x) so that trig(0) = f(0) = 1,
trig '(0) = f '(0) = 1, and trig ''(0) = f ''(0) = -1.
Graph the function trig and find
.
B. Find a quadratic polynomial function q(x) so that q(0) = f(0)
=1, q '(0) = f '(0) = 1, and q ''(0) = f ''(0) = -1.
Graph the function q and find
.
3. Suppose f is a function with f (0) = 1, f '(0) = 1, f ''(0)
= 1, f '''(0) = 1, and f ''''(0)=1.
A. Find a quadratic polynomial function q(x) so that q(0) = f(0)
= 1, q '(0) = f '(0) = 1, and q ''(0) = f ''(0) = 1.
Graph the function q and find
.
B.Find a cubic polynomial function c(x) so that c(0) = f(0) = 1, c
'(0) = f '(0) = 1, c ''(0) = f ''(0) = 1, and c '''(0) = f '''(0) = 1.
Graph the function c and find
.
C. Find a quartic polynomial function r(x) so that r(0) = f(0) = 1,
r '(0) = f '(0) = 1, r ''(0) = f ''(0) = 1, r '''(0) = f '''(0) =
1, and r ''''(0) = f ''''(0) = 1.
Graph the function r and find .
The initial rate of this reaction was measured at 25° C, as a function of initial concentrations (in M) of A, B, and C. The data are as follows:
Trial | [A]_0 | [B]_0 | [C]_0 | Initial Rate (in M/s) |
---|---|---|---|---|
#1 | 0.02 | 0.02 | 0.02 | 1.414 |
#2 | 0.06 | 0.02 | 0.02 | 12.726 |
#3 | 0.06 | 0.06 | 0.02 | 4.242 |
#4 | 0.03 | 0.06 | 0.03 | 1.299 |