Homework 1.1. (a) Find the solution of the initial value problem
x' = x^(3/8) , x(0)=1 , for all t, where x = x(t). (b) Find the
numerical solution on the interval 0 ≤ t ≤ 1 in steps of h = 0.05
and compare its graph with that of the exact solution. You can do
this in Excel and turn in a printout of the spreadsheet and
graphs.
Part A. Find the horizontal and vertical asymptotes of ?(?)=
(6x^2) / (7(x^2 + 8))
Part B. Find the horizontal and vertical asymptotes
of ?(?)= (x^2 - 3) / (x^2 + 2x - 8)
Part C. Find the horizontal and vertical asymptotes of ?(?)=
(x^2 - 49) / (3x^2 - 75)
Part D. Find the horizontal and vertical asymptotes of ?(?)=
(x^3 - 6) / (x^2 + 14x + 49)
For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the
following, and use it to graph the function.
Find: a)(2pts) Domain
b)(2pts) Intercepts
c)(2pts) Symmetry
d) (2pts) Asymptotes
e)(4pts) Intervals of Increase or decrease
f) (2pts) Local maximum and local minimum values
g)(4pts) Concavity and Points of inflection and
h)(2pts) Sketch the curve
Solve the following initial value problems:
a) ut+xux= -tu, x is in R, t>0; u(x,0) =f(x), x is in R.
c) ut+ux=-tu, x is in R, t>0; u(x,0)=f(x), x is in R
d)2ut+ux = -2u, x,t in R, t>0; u(x,t)=f(x,t) on the straight
line x = t, where f is a given function.