Question

HW2:

Q1: find the multiplicity of the root

f(x)=((x-3)^2)*(ln(x-2))

Answer #1

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The polynomial of degree 4, P(x) has a root of multiplicity 2 at
x=2 and roots of multiplicity 1 at x=0 and x=-4 It goes through the
point (5,324).
Find a formula for P(x)

please show all work so i can understand
Write f(x)=ln((x^2 square root(x-4)/(x+1)^3)) in terms of lnx,
ln(x+1), and ln(x-4). Then find f '(x).

Newton's method: For a function ?(?)=ln?+?2−3f(x)=lnx+x2−3
a. Find the root of function ?(?)f(x) starting with
?0=1.0x0=1.0.
b. Compute the ratio |??−?|/|??−1−?|2|xn−r|/|xn−1−r|2, for
iterations 2, 3, 4 given ?=1.592142937058094r=1.592142937058094.
Show that this ratio's value approaches
|?″(?)/2?′(?)||f″(x)/2f′(x)| (i.e., the iteration converges
quadratically). In error computation, keep as many digits as you
can.

Find the derivative of f(x) = 3^(x ln x) and f(x) = ln( 1/ x ) +
1/ ln x

Find derivatives (Please show work!)
1. f(x)=ln(5x^3)
2. f(x)=(ln^3)x
3. f(x)=e^(5x2+2)
4. f(x)=xe^2x
5. f(x)=xlnx

Find the derivative of the given expression.
f(x)=17x^2+ln(x^3)
f'(x)=
Solve the following equation for x:
ln(x−4)+ln(x−2)=ln(8)ln(x−4)+ln(x−2)=ln(8)
If more than one solution exists, separate your answers with a
comma.

Find the derivative of the function.
(a) f(x) = ln (x) + 6x^(2) – 5
(b) f(x) = ln (x + 1)
(c) f(x) = 5 ln x
(d) f(x) = ln(x^(3) – 5x^(2) – 2x + 5)
(e) 2lnx / x
(f) x^(2) ln x

Find a polynomial function with zeros x = 5 with
multiplicity 1 and x = -1 with multiplicity 2 and
x = 8 with multiplicity 3.
f(x) =

Let f(x, y) = x^2 ln(x^3 + y).
(a) Find the gradient of f.
(b) Find the direction in which the function decreases most
rapidly at the point P(2, 1). (Give the direction as a unit
vector.)
(c) Find the directions of zero change of f at the point P(2,
1). (Give both directions as a unit vector.)

Find the Maclaurin series for f(x) = ln(x + 3).

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