1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Evgen [1.6K]
2 years ago
9

What is Difference Quotient used for in real life?

Mathematics
1 answer:
Vitek1552 [10]2 years ago
4 0
What they're going to do is use that formula, then let h get very small ... so small, in fact, that goes to zero "in the limit." And when you do that, you're doing elementary calculus.

Here's an example. Let's take a simple quadratic like y = x^2. This is a parabola that opens upward, but it's curving all the way. It passes through the point (2, 4), and the question is to find the slope of the line tangent to the curve at that point. (The tangent tells you the direction that the curve is pointed. This direction, of course, keeps changing.)

So we have y = f(x) = x^2, and we have your formula [f(x+h) - f(x)] / h.

[f(x+h) - f(x)] / h = [(x+h)^2 - x^2] / h = [(x^2 + 2hx + h^2) - x^2] / h = (2hx + h^2) / h = 2x + h

h is a very small number -- something like h = 0.0000000001. It's so small that you can let it go to zero without losing much, something like this, at x=2 from above:

[f(x+h) - f(x)] / h = 2x + h = 2 • 2 + 0.0000000001 = 4.0000000001 ==> 4

What you've shown is that the slope of y = x^2 at any point (x, y) is 2x. At the point (2, 4), the slope of the curve is 4.

That's elementary calculus, and it all starts with your difference quotient formula.


Does this help?
You might be interested in
In this lesson, the graph of a line is used to find which of the following?
Artemon [7]
All of the above. The graph of a line shows a point on the line, (x,y). It shows the slope (rise/run) it also shows the equation in point-slope form/slope intercept form.
(Slope intercept and point-slope are the same equation, but in a different form.)
6 0
2 years ago
Read 2 more answers
sofia can paint a house in 10 hours juana can paint the same in 9 hours how long would it take them if they worked together
lubasha [3.4K]
If Sofia and Juana worked together I would take them 1 hour
7 0
3 years ago
What is the rate of change of the linear function represented by the table? StartFraction one Over three EndFraction StartFracti
Lynna [10]

The rate of change of the linear function represented by the table is 3

<h3>Rate of change of a function</h3>

The rate of change of a function is also known as the slope of a function. The equation for calculating the slope is expressed as:

Slope = y2-y1/x2-x1

using the coordinates from the table (-2, -13) and (-1, -10)

Substitute

Slope = -10-(-13)/-1-(-2)

Slope = -10+13/-1+2

Slope =3

Hence the rate of change of the linear function represented by the table is 3

Learn more on rate of change here: brainly.com/question/25184007

#SPJ1

5 0
2 years ago
Find the number of pairs (a,b) of integers such that<br> a+2/a+5=b/3
Viktor [21]

Answer:

  6

Step-by-step explanation:

The expression can be rearranged to ...

  b = 3 -9/(a+5)

In order for b to be an integer, (a+5) must be an integer divisor of 9. There are exactly 6 of those: ±1, ±3, ±9.

The attached table shows the values (a, b) = (x₁, f(x₁)).

3 0
3 years ago
Use the drop-down menus to identify the parts of the pyramid.
sveticcg [70]

Answer:

D corresponds to the base.

Ethire C or A corresponds to the height.

I'm sorry, that's all I know. I'm new to this kind of math.

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • What is the solution to the system of equation? Y=-5x+3 y=1
    7·2 answers
  • A dance school charges a registration addition to a fee per lesson. The equation is y=30x+25 represents the total cost x lessons
    14·2 answers
  • (5) Blackbeard and Shamus find a treasure chest with $40,000 in coins inside. Blackbeard takes
    10·1 answer
  • Factor completely x2 + 25.
    7·2 answers
  • James, Priya, and Siobhan work in a grocery store. James makes $8.00 per hour. Priya makes 40% more than James, and Siobhan make
    5·1 answer
  • Thx u help now ok yeah
    10·1 answer
  • Help me with that asap
    8·1 answer
  • Eva has a coupon for an oil change with synthetic oil for $59.95. She can buy 5 quarts of synthetic oil, which is what her car n
    6·1 answer
  • Which of the following represents discrete data? Question 7 options: The number of beads in a jar The volume of water in a glass
    9·1 answer
  • In the graph, what fraction does the arrow point to? ​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!