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kicyunya [14]
3 years ago
12

Find the limit of the function by using direct substitution. limit as x approaches one of quantity x squared plus three x minus

one.
Mathematics
1 answer:
ivann1987 [24]3 years ago
6 0

<u>Answer:</u>

Limit = -1

<u>Step-by-step explanation:</u>

We are given the following function:

x^2 + 3x -1

We are to calculate the limit of this function as x approaches zero.

For that, we will use direct substitution method and substitute the x with 0 in the given function to calculate its limit as follows:

x ^ 2 + 3 x - 1

( 0 ) ^ 2 + 3 ( 0 ) - 1 = - 1

Therefore, the limit is -1.

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Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive
Ivan

Answer:

(a) The average cost function is \bar{C}(x)=95+\frac{230000}{x}

(b) The marginal average cost function is \bar{C}'(x)=-\frac{230000}{x^2}

(c) The average cost approaches to 95 if the production level is very high.

Step-by-step explanation:

(a) Suppose C(x) is a total cost function. Then the average cost function, denoted by \bar{C}(x), is

\frac{C(x)}{x}

We know that the total cost for making x units of their Senior Executive model is given by the function

C(x) = 95x + 230000

The average cost function is

\bar{C}(x)=\frac{C(x)}{x}=\frac{95x + 230000}{x} \\\bar{C}(x)=95+\frac{230000}{x}

(b) The derivative \bar{C}'(x) of the average cost function, called the marginal average cost function, measures the rate of change of the average cost function with respect to the number of units produced.

The marginal average cost function is

\bar{C}'(x)=\frac{d}{dx}\left(95+\frac{230000}{x}\right)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g\\\\\frac{d}{dx}\left(95\right)+\frac{d}{dx}\left(\frac{230000}{x}\right)\\\\\bar{C}'(x)=-\frac{230000}{x^2}

(c) The average cost approaches to 95 if the production level is very high.

\lim_{x \to \infty} (\bar{C}(x))=\lim_{x \to \infty} (95+\frac{230000}{x})\\\\\lim _{x\to a}\left[f\left(x\right)\pm g\left(x\right)\right]=\lim _{x\to a}f\left(x\right)\pm \lim _{x\to a}g\left(x\right)\\\\=\lim _{x\to \infty \:}\left(95\right)+\lim _{x\to \infty \:}\left(\frac{230000}{x}\right)\\\\\lim _{x\to a}c=c\\\lim _{x\to \infty \:}\left(95\right)=95\\\\\mathrm{Apply\:Infinity\:Property:}\:\lim _{x\to \infty }\left(\frac{c}{x^a}\right)=0\\\lim_{x \to \infty} (\frac{230000}{x} )=0

\lim_{x \to \infty} (\bar{C}(x))=\lim_{x \to \infty} (95+\frac{230000}{x})= 95

6 0
3 years ago
A slug travels 3 centimeters in 3 seconds. A snail travels 6 centimeters in 6 seconds. Both travel at constant speeds. Mai says,
ollegr [7]

Answer:

Mai is wrong since both travel the same distance in the same amount of seconds

Step-by-step explanation:

3 centimeters in 3 seconds is 1 centimeter a second for the slug

6 centimeters in 6 seconds is 1 centimeter a second for the snail

so both travel the same distance

5 0
3 years ago
Read 2 more answers
Sally has made a scale drawing of the airplane, in which the wingpsan is 10 inches and the tailspan is 3 inches. What is the act
labwork [276]
The answer would be a
7 0
2 years ago
Suppose you invest $16000 at 9% interest and that it is compounded daily. How much will you have in 8 years?
kramer

Answer:

The amount after 8 years is $ 16,031.579

Step-by-step explanation:

Given as :

The Principal invested = $ 16000

The rate of interest compounded daily = 9 %

The time period = 8 years

Let The amount after 8 years = $ A

<u>From Compounded method </u>

Amount = Principal invested × (1+\dfrac{\textrm Rate}{365\times 100})^{365\times \textrm Time}

Or, Amount = 16000 × (1+\dfrac{\textrm 9}{365\times 100})^{365\times \textrm 8}

Or, Amount = 16000 × (1.0002465)^{8}

∴  Amount = $ 16,031.579

Hence The amount after 8 years is $ 16,031.579   Answer

4 0
3 years ago
Victor always runs out of money by the end of the month, so he wants to start keeping a budget. Last month, he spent a total of
Sholpan [36]

Answer:

Yearly budget= $3840

Monthly budget= $320

Step-by-step explanation:

His budget will be calculated first by rounding off to the nearest$10 all his monthly spending.

For groceries= $176.47

Round off=$ 180.00

For phone =$ 78.66

Round off = $80.00

For gas = $62.37

Round off= $60.00

His total round off = $180+$80+$60

His total round off = $320

Before the round off, his total spending was $176.47+$78.66+$62.37

= $317.5

So his monthly budget should be $320

And yearly budget =$ 320*12

Yearly budget= $3840

4 0
3 years ago
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