Question

a.

Explain, using the power rule, why the antiderivative of f (x)= 1/x is F(x) = ln |x| + c , but the antiderivative of f(x)= 1/x^2 is NOT F(x)=ln |x^2| + c.

Answer #1

Find a power series representation for the function.
f(x) = ln(5 − x)
f(x) = ln(5) +
∞
(−1)nn(x5)n
n = 0
Determine the radius of convergence, R.
R =

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

Evaluate the following:
1) ∫ 4? ?? and determine C if the antiderivative F(x) satisfies
F(2) = 12.
2) ∫4???=
3) ∫( ?5 + 7 ?2 + 3 ) ?? =
4) ∫ ?4( ?5 + 3 )6 ?? =
5)∫4?3 ??=?4+ 3
6) ∫ ?2 sec2(?3) ?tan(?3)??
7 ) ∫ 53 ? 13 ? ? =
8) ∫ ln8(?) ?? =?
9) ∫ 3 ln(?3) ?? =?
10) ∫ 4?3 sin3(?4) cos(?4) ?? =
11) ∫6?55?6??=
12) ∫???2(3?)??=
13)...

Find a power series representation for f(x) = ln(x^7 + 2), and
find its radius of convergence.

Find the antiderivative
f(x) = 3x^2 + 4x + 5
f(x) = 3 cos x
f(x) = e^2x + 4x^3
f(x) = sec^2 x

1) Find the antiderivative if f′(x)=x^6−2x^−2+5 and f(1)=0
2)Find the position function if the velocity is v(t)=4sin(4t)
and s(0)=0

let
f(x)=ln(1+2x)
a. find the taylor series expansion of f(x) with center at
x=0
b. determine the radius of convergence of this power
series
c. discuss if it is appropriate to use power series
representation of f(x) to predict the valuesof f(x) at x= 0.1, 0.9,
1.5. justify your answe

approximate the value of ln(5.3) using fifth degree taylor
polynomial of the function f(x) = ln(x+2). Find the maximum error
of your estimate.
I'm trying to study for a test and would be grateful if you
could explain your steps.
Saw comment that a point was needed but this was all that was
provided

Consider the following function.
f(x) =
x4 ln(x)
a.) Use l'Hospital's Rule to determine the limit as
x → 0+
b.) Use calculus to find the minimum value.
c.) Find the interval where the function is concave down. (Enter
your answer in interval notation.)

(a) Find the most general antiderivative of the function f(x) =
−x^ −1 + 5√ x / x 2 −=4 csc^2 x
(b) A particle is moving with the given data, where a(t) is
acceleration, v(t) is velocity and s(t) is position. Find the
position function s(t) of the particle. a(t) = 12t^ 2 − 4, v(0) =
3, s(0) = −1

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