Question

Find the Wronskian of the three functions to determine if they
are linearly independent. Include enough steps so that I can follow
your work. **f(x) = x; g(x) = sin(x); h(x) =
e ^{x}**.

Answer #1

Determine whether the given functions are linearly dependent or
linearly independent.
f1(t) =
4t − 7,
f2(t) =
t2 + 1,
f3(t) =
6t2 − t,
f4(t) =
t2 + t + 1
linearly dependentlinearly independent
If they are linearly dependent, find a linear relation among them.
(Use f1 for f1(t),
f2 for f2(t),
f3 for f3(t), and
f4 for f4(t).
Enter your answer in terms of f1,
f2, f3, and
f4. If the system is independent, enter
INDEPENDENT.)

The indicated functions are known linearly independent solutions
of the associated homogeneous differential equation on (0, ∞). Find
the general solution of the given nonhomogeneous equation.
x2y'' + xy' + y = sec(ln(x))
y1 = cos(ln(x)), y2 = sin(ln(x))

Show whether the following vectors/functions form linearly
independent sets:
(a) 2 – 3x, x + 2x^2 , – x^2 + x^3
(b) cos x, e^(–ix), 3 sin x
(c) (i, 1, 2), (3, i, –2), (–7+i, 1–i, 6+2i)

Mr. Optimal wants to find the values of x ? [0, 2?] that
minimize the functions f(x) = sin(x), g(x) = 5 sin(x), and h(x) =
sin(5x) using Generalized Pattern Search. Please sort the functions
(i.e., f, g, and h) based on the difficulty of finding the desired
value using Generalized Pattern Search, and please explain your
answer.

1. Differentiate the following functions. Do not simplify.
(a) f(x) = x^7 tan(x)
(b) g(x) = sin(x) / 5x + ex
(c) h(x) = (x^4 + 3x^2 - 6)^5
(d) i(x) = 4e^sin(9x)
(e) j(x) = ln(x) / x5
(f) k(x) = ln(cot(x))
(g) L(x) = 4 csc^-1 (x2)
(h) m(x) = sin(x) / cosh(x)
(i) n(x) = 2 tanh^-1 (x4 + 1)

Determine if the set of functions is linearly independent:
1. f1(x)=cos2x, f2(x)=1, f3(x)=cos^2 x
2. f1(x)=e^ x, f2(x)=e^-x, f3(x)=senhx

Find the derivatives of each of the following functions. DO NOT
simplify your answers.
(a) f(x) = 103x (3x5+ x − 1)4
(b) g(x) = ln(x3 + x) /
x2 − 4
(c) h(x) = tan-1(xex)
(d) k(x) = sin(x)cos(x)

1 point) Find the work done by F along different paths between
(1,0,1) and (1,1,0).
You might simplify your computation by writing F=G+H=∇g+H, so
that you have a decomposition ofFF into a conservative vector field
and a simpler non-conservative vector field.
F=〈e^(yz)+2y, xze^(yz)+zcos(y)−3z, xye^(yz)+sin(y)−2x〉
(a) The path is the straight line path between those two points.
(Hint: the answer is not 2, 4, or 0.)
Work is .
(b) The path consists of the line segment from (1,0,1) to the
origin,...

Find and sketch domains for the functions:
f(x,y)= sin(x/y)
f(x,y)= arcsin(x/y)
f(x,y)=cos(x/y)
f(x,y)=arccos(x/y)
What are the steps of finding the domain of those functions?
How do I sketch it?

Q 1) Consider the following functions.
f(x) = 2/x, g(x) = 3x + 12
Find (f ∘ g)(x).
Find the domain of (f ∘ g)(x). (Enter your answer using interval
notation.)
Find (g ∘ f)(x).
Find the domain of (g ∘ f)(x). (Enter your answer using
interval notation.)
Find (f ∘ f)(x).
Find the domain of (f ∘ f)(x). (Enter your answer using
interval notation.)
Find (g ∘ g)(x).
Find the domain of (g ∘ g)(x). (Enter your answer using interval
notation.)
Q...

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