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Julli [10]
2 years ago
11

I need the answers and it's due today, please help

Mathematics
1 answer:
Novay_Z [31]2 years ago
3 0

Answer:

1. 3

2. 1

3. 2

4. 4

5. 5

Step-by-step explanation:

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What is the essence of calculus? <br>*friendship​
iragen [17]

Differential Calculus, or Differentiation

If we have a function of one variable, ie of the form y=f(x), then in its most basic form differentiation is the study of how a small change in one variable x affects the other variable y.

As an real life example, consider the average speed of a moving car:

average speed = distance travelled/ time taken

Obviously, this is an average by definition, but if there existed a formal mathematical link between distance and time, could we build a function that would tell us the instantaneous velocity at every given moment? The study of differential calculus gives strategies for calculating the ratio of a little change in distance to a small change in time, and then calculating the real instantaneous speed by making the small change infinitely small.

Similarly if we wanted to find the gradient of the tangent to a curve at some particular point A we would estimate the gradient by using a chord to a nearby point B. As we move this nearby point B  closer to the tangent point A the slope of the chord approaches the slope of the tangent with more and more accuracy. Again differential calculus provides techniques for us to make the point B infinitesimally close to the point A o that we can calculate the actual gradient of the tangent.

Integral Calculus, or Integration

Suppose we wanted to calculate the area under a curve, y=f(x),  bounded the x =axis, and two points a and b. We could start by splitting the interval  [a,b]  into n regular strips, and estimating the area under the curve using trapezia (this is the essence of the trapezium rule which provides an estimate of such an area). If we increase n then generally we would hope for a better approximation. The study of integration provides techniques for us to take an infinitely large number of infinitesimally small strips to gain an exact solution.

The Fundamental Theorem of Calculus

Given the above two notions, it would appear that there is no connection between them at first., The Fundamental Theorem of Calculus, on the other hand, is a theorem that connects the rate of change of the area function (which determines the area under a curve) to the function itself. In other words, the area function's derivative equals the function itself.

Visual for  Fundamental Theorem of Calculus for integrals:

\int\limits^b_af {(x)} \, dx =F(b)-F(a).

where F is an antiderivative of f

Physics, Chemistry, all engineering sciences, statistics, economics, finance, biology, computer science, linguistics, to name but a few, are all areas that would be a desert without the use of calculus.

Leibnitz and Newton worked to define the velocity of a planet moving on a curved trajectory. That was not possible without calculus, and both had to invent differential calculus. Differential calculus allows to compare quantities along a curve, and thus their time rate of change.

All of classical physics can be summarized in this operation. Given second derivative (which is Force/mass), find the position as a function of time. This process is called integration. Half of calculus is made with integration, the other half with derivation. All of classical physics rests on these two parts of the calculus.

Quantum mechanics, quantum field theory, electromagnetism, fluid mechanics all use integration and derivation and much more. I rest my case. I hope this helps you gauge the place that calculus occupies in science.

4 0
1 year ago
Read 2 more answers
A scalene triangle is obtuse. <br> Determine if the statement is always, sometimes, or never true.
valentina_108 [34]

Answer:

sometimes

Step-by-step explanation:

4 0
3 years ago
How do mental math strategies help you solve problems such as the ones above?
Luden [163]

With mental math, you can perform equations quickly and efficiently. They also help you to develop your own strategies and solve more complex math equations. Hope this helps;)


7 0
3 years ago
Find the height of a parallelogram with an area of 56 and a base of 20.
qaws [65]
The correct answer is 2.8
6 0
3 years ago
Tia measured the daily high temperature in Kats, Colorado for each of the 30 days in April. She then created both a dot plot and
lara31 [8.8K]

*see attachment below showing the dot plot and box plot created by Tia

Answer:

Dot plot

Step-by-step explanation:

In a dot plot, the temperature of a day is represented by 1 dot. There are 30 dots on the box plot shown in the attachment that was made by Tia.

This dot plot display makes it easier to find how many days had a temperature that is higher than 15°.

Thus, from the dot plot, we have:

2 dots representing 2 days having a temperature of 16°C each

2 days also have daily temperature of 17°C

2 days have temperature of 18°C as well, and

1 day has temperature of 19° C.

Therefore, the number of days that had a temperature above 15°C is 7 days.

3 0
3 years ago
Read 2 more answers
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