find the radius of convergence and interval of convergence of the series ∑ n=1 ~ ∞ (3^n)((x+4)^n) / √n

Please solve this problem with detailed process of solving.

I can't understand why the answer is [-13/3, -11/3)

I thought that the answer was (-13/3, -11/3].

Can you explain why that is the answer?

A plane delivers two types of cargo between two destinations. Each crate of cargo I is 7 cubic feet in volume and 131 pounds in weight, and earns $20 in revenue. Each crate of cargo II is 7 cubic feet in volume and 262 pounds in weight, and earns $25 in revenue. The plane has available at most 525 cubic feet and 12,576 pounds for the crates. Finally, at least twice the number of crates of I as II must be shipped. Find the number of crates of each cargo to ship in order to maximize revenue. Find the maximum revenue.

A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $2/unit of Product A and a profit of $4/unit of Product B. To manufacture a unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of machine time available on Machine I and 3 hr of machine time available on Machine II in each work shift. How many units of each product should be produced in each shift to maximize the company's profit?

What is the optimal profit? (Round your answer to the nearest whole number.)
$

Using limit to find the equation of the tangent line to the curve y = f(t)=2t^3+3t at the point Q(1,5)

y=x^5 - 5x

Use the "Guidelines for sketching a curve A-H"

A.) Domain
B.) Intercepts
C.) Symmetry
D.) Asymptotes
E.) Intervals of increase or decrease
F.) Local Maximum and Minimum Values
G.) Concavity and Points of Inflection
H.) Sketch the Curve

1. Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = x³ + y³ − 3x² − 6y² − 9x

2. Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = 3x³ − 9x + 9xy²

^3. Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f (x, y) = xy − 3x − 3y − x² − y²

3. Jose deposits $150 at the end of each
month into an account that pays 6%
interest compounded monthly . After 8
years of deposits, what is the account
balance?

Prove the following using the method suggested:
(a) Prove the following either by direct proof or by contraposition:
Let a ∈ Z, if a ≡ 3 (mod 5) and b ≡ 2 (mod 5), then ab ≡ 1 (mod 5).

(b) Prove the following by contradiction:
Suppose a, b ∈ Z. If a² + b²
is odd, then (2|a) ⊕ (2|b), where ⊕ is the exclusive disjuntion,
i.e. p ⊕ q = (p ∨ q) ∧ ¬(p ∧ q).

(d) Prove the following by cases: For all n ∈ Z, n
2 + 3(n + 1) is odd.

(e) Prove the following by induction:
For n ≥ 1,
1 × 2 + 2 × 3 + 3 × 4 + · · · + n(n + 1) = n/3
(n + 1)(n + 2)

C. Clearly indicate the plate number and indexing movements to be made to divide the periphery of a work piece into 29 divisions using compound Indexing? The following indexing plates are available. Plate No 1: 15,16,17,18,19,20.: Plate No 1: 21,23,27,29,31,33. Plate No 1: 37,39,41,43,45,49

Evaluate the integral by making an appropriate change of variables.

where R is the trapezoidal region with vertices (6, 0), (10, 0), (0, 10), and (0, 6)

Differentiate each. give reasonably simplified answers. Box ANSERS.

(a)=ln[(x^9*(5x+1)^4*(11x+2))/((8x+9)(3x^5-2x+1))]

(b) y=log[((8x+3)^2 * (x^3+5x^2-9x+1))/(7x+3)^5]

(c) Given f(x)=(4x)^10x^3, find f'(x)

(d) Differentiate f(x)=4x^10x^3, find f'(x)

please graph the function f(x)=(x-2)/(x-1) by finding

the domain
the x and y intercepts
the vertical asymptotes
the horizontal asymptotes
the intervals of increase and decrease
the local mins/max
the intervals of concavity
the inflection point(s) as an ordered pair

Solve the differential equation dy/dx = 15x + 5y/ 5x + 15y.

Write your solution without logarithms, and use a single, consolidated c as a constant

If a circle C with radius 1 rolls along the outside of the circle x² + y² = 36, a fixed point P on C traces out a curve called an epicycloid, with parametric equations x = 7 cos(t) − cos(7t), y = 7 sin(t) − sin(7t). Graph the epicycloid.

Find the area it encloses.