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yuradex [85]
3 years ago
10

PLEASE HELP ME 40 PTS!!!!!!

Mathematics
1 answer:
SSSSS [86.1K]3 years ago
8 0

Answer:

The sequence converges to  infinity.

Step-by-step explanation:

a_n = \frac{n^3 - n}{n^2 + 5n}\\\\ \lim_{n \to \infty} a_n  =  \lim_{n \to \infty} \frac{n^3 - n}{n^2 + 5n}

                = \lim_{n \to \infty} \frac{n(n^2 - 1)}{n(n + 5)} \\\\= \lim_{n \to \infty} \frac{(n^2 - 1)}{(n + 5)}\\\\= \lim_{n \to \infty} \frac{n(n - \frac{1}{n})}{n(1 + \frac{5}{n})}\\\\= \lim_{n \to \infty} \frac{(n - \frac{1}{n})}{(1 + \frac{5}{n})}

denominator =  \lim_{n \to \infty}  1 + \frac{5}{n} = 1 +  \lim_{n \to \infty} \frac{5}{n} = 1+0 = 1

numerator =  \lim_{n \to \infty} n - \frac{1}{n} = \infty

Therefore,

             \lim_{n \to \infty} a_n  = \frac{ \infty}{1} = \infty

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Let g be the function given by g(x)=limh→0sin(x h)−sinxh. What is the instantaneous rate of change of g with respect to x at x=π
lorasvet [3.4K]

The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>.

<h3>How to determine the instantaneous rate of change of a given function</h3>

The <em>instantaneous</em> rate of change at a given value of x can be found by concept of derivative, which is described below:

g(x) =  \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}

Where h is the <em>difference</em> rate.

In this question we must find an expression for the <em>instantaneous</em> rate of change of g if f(x) = \sin x and evaluate the resulting expression for x = \frac{\pi}{3}. Then, we have the following procedure below:

g(x) =  \lim_{h \to 0} \frac{\sin (x+h)-\sin x}{h}

g(x) =  \lim_{h \to 0} \frac{\sin x\cdot \cos h +\sin h\cdot \cos x -\sin x}{h}

g(x) =  \lim_{h \to 0} \frac{\sin h}{h}\cdot  \lim_{h \to 0} \cos x

g(x) = \cos x

Now we evaluate g(x) for x = \frac{\pi}{3}:

g\left(\frac{\pi}{3} \right) = \cos \frac{\pi}{3} = \frac{1}{2}

The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>. \blacksquare

To learn more on rates of change, we kindly invite to check this verified question: brainly.com/question/11606037

4 0
2 years ago
Berry Delicious is a popular shop that sells chocolate-covered strawberries. Last year, the shop used 9,200 kilograms of strawbe
coldgirl [10]

Answer:

15.9%

Step-by-step explanation:

Percent decrease formula =

(Initial value - New value/Initial value) × 100

Initial value = 9200kg

New value = 7739.4kg

Percent decrease = (9200 - 7739.4/9200) × 100

Percent decrease = (1460.6/9200) × 100

Percent decrease = 15.8760869565%

Approximately = 15.9%

The percent of decrease in the amount of strawberries used annually is 15.9%

6 0
3 years ago
If the sum of three consecutive numbers is 852, what is the middle one?
denis-greek [22]

Divide the total by the quantity of numbers:

852/3 = 284

Because there are an odd quantity of numbers (3) the answer is the middle number.

The answer is 284

5 0
3 years ago
The chord XY is a diameter of of O. True or false?
steposvetlana [31]

Answer:

False

Step-by-step explanation:

XY is the diameter of the circle with the centre of this circle being O.

But O on it's own is just a coordinate, and not the circle.

3 0
3 years ago
Read 2 more answers
Write an expression that represents the sum of x and 8
krok68 [10]

Answer:

x+8

Step-by-step explanation:

we know that

The phrase " the sum of x and 8" is equivalent to adds the number x and the number 8 or sum the number x plus the number 8

so

x+8

6 0
3 years ago
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