Question

a)Describe the connection between the kth divided difference of a function f and its kth derivative.

b)State one advantage and two disadvantages of using the monomial basis for polynomial interpolation.

Answer #1

Using the central divided difference approximation with a step
size of 0.4, the derivative of f(x) = 6x^4 at x = 2.1 is ____. Keep
4 decimal places.

Derive or prove the three point backward difference
approximation of the first derivative, aka Dh--f, of a
function f(x), using either polynomial interpolant method (Newton's
or Lagrange's) here is the first derivative approximation: f'(x) =
(3* f(x) - 4*f(x-h)+ f(x-2h)) /2h , which is congruent to
Dh--f

In class I gave a general formula for derivative of an
exponential function f(x) = loga u(x); where "a" is
called Base, and u(x) is called the argument of the log function,
which is also given below.
Note, the derivative of a logarithmic function f(x) has three
parts and is given here:
f ' (x) = 1/ln (a) . 1/u(x) . u ' (x)
In your words, describe (in words only) each one of
the three parts shown above:
a- describe...

For each polynomial f(x) ∈ Z[x], let f ' (x) denote its
derivative, which is also a polynomial in Z[x]. Let R be the
following subset of Z[x]: R = {f(x) ∈ Z[x] | f ' (0) = 0}. (a)
Prove that R is a subring of Z[x]. (b) Prove that R is not an ideal
of Z[x].

Let f(x,y) be a function of x and y. The partial derivative of
f(x,y) with respect to y is equivalent to the directional
derivative of f(x,y) in the direction of the unit vector
Select one:
a. 〈0,1〉
b. 〈1,0〉
c. 〈1,1,1〉
d. 〈0,5〉

1. Consider the function.
f(x) = 6x − 9
(a) Find the inverse function of f.
(b) Graph f and f −1 on the same
set of coordinate axes.
(c) Describe the relationship between the graphs. The graphs of
f and f −1 are reflections of each
other across the line y =
(d) State the domain and range of f and f
−1. (Enter your answers using interval notation.)
2.
Consider the function.
f(x) = x+3/x
(a) Find the...

For
function, f(z)=ze^z
use Cauchy-Reimann equations to see if its analytic and find
the derivative of f(z)

Consider f(x) = x2 – 8x. Find its derivative using
the limit definition of the derivative. Simplify all
steps.
a. Find f(x + h).
____________
b. Find f(x + h) – f(x).
____________
c. Find [f(x + h) – f(x)] ÷ h.
____________
d. Find lim (hà0) [f(x + h) – f(x)] ÷ h.
____________
e. Find an equation of the line tangent to
the graph of y = x2 – 8x where x = -3. Present your
answer...

Nonprofits can develop budgets for general operations and
capital spending. Describe the difference between these two
different budgets. Why do nonprofits develop two different budgets?
What are some advantages and disadvantages of having separate
operations and capital budgets?

list the components of a reflex arc and describe a nerve pathway.
explaib the difference between pathways in the SNS and ANS.
describe the structure and function of the meninges.
identify the cranial nerves and relate each nerve to its
principal destinations and functions.

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