Answer the following using Binomial theorem and Pascal's
Triangle:
a. Find the middle term in the expansion of (4x –
x3)14
b. Use Pascal’s triangle to expand (3x +
2y)6.
Rewrite your program for finding Pascal's Triangle to use
iteration (loops) instead of recursion. Include in both algorithms
code to keep track of the total time used to run the algorithms in
milliseconds. Run these algorithms for n = 10, n = 20, and n = 30.
Print out both the original output and the time to run for both
algorithms. Please make sure you comment your code thoroughly. The
code should be nicely formatted and should use proper
variables.
Expand in Fourier series:
Expand in fourier sine and fourier cosine series of: f(x) =
x(L-x), 0<x<L
Expand in fourier cosine series: f(x) = sinx, 0<x<pi
Expand in fourier series f(x) = 2pi*x-x^2, 0<x<2pi,
assuming that f is periodic of period 2pi, that is,
f(x+2pi)=f(x)
Prove for the system of ordinary differential equations x'=-x,
and y'=-5y the origin is lyapunov stable, attracting and
asymptotically stable using the EPSILON DELTA definition of each.
The epsilon and delta that make the definitions hold must be
found.
f(x,y) = 2/7(2x + 5y) for 0 < x < 1, 0 < y < 1
given X is the number of students who get an A on test 1
given Y is the number of students who get an A on test 2
find the probability that more then 90% students got an A test 2
given that 85 % got an A on test 1
PROVIDE EXPLANATION
2. Elmer’s utility function is U(x, y) minx, 5y. If the
price of x is $25, the price of y is $10, and Elmer
chooses to consume 5 units of y, what must Elmer’s income be?
a. $1,350
b. $175
c. $775
d. $675
e. There is not enough information to tell.