How do i derive (x^-4) using the limit definition [f(x+h) - f(x) / h]

Answers

Answer 1

Answer: $f'(x)=\lim\limits_(h\to0)(f(x-h)-f(x))/(h)\n\nf(x)=x^(-4)=(1)/(x^4)\n\nf'(x)=\lim\limits_(h\to0)((x+h)^(-4)-x^(-4))/(h)=\lim\limits_(h\to0)((1)/((x+h)^4)-(1)/(x^4))/(h)=\lim\limits_(h\to0)((x^4-(x+h)^4)/(x^4(x+h)^4))/(h)\n\n=\lim\limits_(h\to0)\left[(x^4-x^4-4x^3h-6x^2h^2-4xh^3-h^4)/(x^4(x+h)^4)\cdot(1)/(h)\right]=\lim\limits_(h\to0)(-4x^3h-6x^2h^2-4xh^3-h^4)/(hx^4(x+h)^4)$

$=\lim\limits_(h\to0)(h(-4x^3-6x^2h-4xh^2-h^3))/(hx^4(x+h)^4)=\lim\limits_(h\to0)(-4x^3-6x^2h-4xh^2-h^3)/(x^4(x+h)^4)\n\n=(-4x^3-6x^2\cdot0-4x\cdot0^2-0^3)/(x^4(x+0)^4)=(-4x^3)/(x^4\cdot x^4)=(-4)/(x^5)\n\n\nD_f=D_(f')=\mathbb{R}\ \backslash\ \{0\}$

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How do I write two hundred fifty million in expanded notation using powers of ten

Answers

2.5 x 10^8 I think that's it anyway

there are 8 zeros in a million and the power of ten equals a number per 0 so 2.50 * 10 to the 8th

Josiah went to the barber to get his haircut.It cost $18 for the haircut.Josiah tipped the barber 15%.What was the total cost of the haircut including the tip?

Answers

Answer:

Tip -$2.70

Total -$20.70

Step-by-step explanation:

I need help with 1+1 First answer gets Brainliest(Please explain how you got the answer)

Answers

Answer:

Step-by-step explanation:

The numbers of bees that visit a plant is 500 times the number of years the plant is alive, where t represents the number of years the plant is alive . what does the expression 500t represent

Answers

For this case, the first thing we must do is define variables.

We have then:

t: the number of years the plant is alive

f (t): the numbers of bees that visit the plant

The equation modeling the problem is given by:

Answer:

the expression 500t represent:

the numbers of bees that visit the plant

500t represents the number of bees that visit the plant.

NEED HELP NOW!! Will give 20 extra PTS to the best answercomplete the solution of the equation. Find the value of y when x equals -8.
4x + 9y = -14

Answers

To find the value of y, you need to plug a value into the x variable, in this case -8.

4x + 9y = -14 Substitute -8 for x
4 (-8) + 9y = -14 Multiply
-32 + 9y = -14 Start isolating the variable by adding 32 to both sides
9y = 18 Divide both sides by 9
y = 2

When x = -8, y = 2

Ms. Scott wrote a test. Part A had true/false questions, each worth 6 points. Part B had multiple choice questions, each worth 4 points. She made the number ofpoints for Part A equal the number of points for Part B. It was the least number of points for which this was possible,
Answer the following questions.
How many points was each part worth?
points
How many questions did Part A have?
questions
How many questions did Part B have?
questions

Answers

Answer:

1. How many points was each part worth?

- 12 points

2. How many questions did part A have?

- 2 questions

3. How many questions did Part B have?

- 3 questions

Step-by-step explanation:

We can set up our equation like this:

6x = 4y

In the above equation, x is representing the number of true/false questions and y is representing the nymber of multiple choice questions.

Now, the problem tells us that they want the least number of points possible so we know we need to use low numbers.

Since 6 is higher than 4, it's easier to go off of there.

6 x 1 = 6 4 is too big to go into 6 so we will move on.

6 x 2 = 12 4 goes into 12 3 times so we can use this.

Now that we've figured this out, we can put it in our equation:

6(2) = 4(3)

In the above equation, we can see that I've put 2 in for x because we multiplied 6 by 2 to get 12. I also put 3 in for y because we multiplied 4 by 3.

Now we can start with the questions:

1. How many points was each part worth?

Each part was worth 12 points because we can multiply 6 by 2 and get 12 or 4 by 3 and get the same thing

2. How many questions did part A have?

Part A had 2 questions because this is what x was when we multiplied by 6

3. How many questions did Part B have?

Part B had 3 questions because this is what y was when we multiplied by 4

Hope this helps!!

Final answer:

Each part is worth 12 points. Part A has 2 questions. Part B has 3 questions.

Explanation:

The problem states that the number of points for Part A is equal to the number of points for Part B, and we need to find the least number of points for which this is possible. Let's represent the number of questions in Part A as x. Since each true/false question is worth 6 points, the total points for Part A will be 6x. Similarly, let's represent the number of questions in Part B as y. Since each multiple choice question is worth 4 points, the total points for Part B will be 4y. To find the least number of points for which the two parts are equal, we need to find the smallest common multiple of 6 and 4.

The prime factorization of 6 is 2 x 3.

The prime factorization of 4 is 2 x 2.

From the prime factorization, we can see that the least common multiple (LCM) of 6 and 4 is 2 x 2 x 3 = 12.

Therefore, each part is worth 12 points.

To find the number of questions in Part A and Part B, we can substitute 12 for the total points in each part and solve for x and y:

6x = 12

x = 2

4y = 12

y = 3

Learn more about Least Common Multiple here:

brainly.com/question/34291727

#SPJ2

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