T(1+2x)=1+x-x^2
T(1-x^2)=2-x
T(1-2x+x^2)=3x-2x^2
a)compute T(-6x+3x^2)
b) find basis for N(T), null space of T
c) compute rank of T and find basis of R(T)
The curves of the quadratic and cubic functions are f(x)=2x-x^2
and g(x)= ax^3 +bx^2+cx+d. where a,b,c,d ER, intersect at 2 points
P and Q. These points are also two points of tangency for the two
tangent lines drawn from point A(2,9) upon the parobala. The graph
of the cubic function has a y-intercept at (0,-1) and an x
intercept at (-4,0). What is the standard equation of the tangent
line AP.
The curves of the quadratic and cubic functions are f(x)=2x-x^2
and g(x)= ax^3 +bx^2+cx+d. where a,b,c,d ER, intersect at 2 points
P and Q. These points are also two points of tangency for the two
tangent lines drawn from point A(2,9) upon the parobala. The graph
of the cubic function has a y-intercept at (0,-1) and an x
intercept at (-4,0). What is the value of the coefficient "b" in
the equation of the given cubic function.
1. Consider the cubic function f ( x ) = ax^3 + bx^2 + cx + d
where a ≠ 0. Show that f can have zero, one, or two
critical numbers and give an example of each case.
2. Use Rolle's Theorem to prove that if f ′ ( x ) = 0 for all
xin an interval ( a , b ), then f is constant on ( a , b
).
3.True or False. The product of...
A cubic polynomial is of the form: f(x) = Ax^3 + Bx^2 + Cx + D
A root of the polynomial is a value, x, such that
f(x)=0.
Write a program that takes in the coefficients of a cubic
polynomial: A, B, C, and D. The program finds and reports all three
roots of the polynomial.
Hint: First use bisection method to determine a single root of
the polynomial. Then divide the polynomial by its factor to come up...
The system: 2A + B ↔ 2C ; initially started with 1 mole of B and
1 mol A in a 1L flask. Keq = 6.8 x 10-5 To
calculate the equilibrium concentrations a simplifying assumption
(approximation) can be made.
True
False
Show that the AR(2) process Xt=X(t-1)+cX(t-2)+Zt is stationary
provided by-1<c<0. Find the autocorrelation function when
c=-3/16. Show that the AR(3) process Xt=X(t-1)+cX(t-2)-cX(t-2)+Zt
is non-stationary for all values of c.