Can you give me some calculus example. What i mean is real life useage of calculus.?

Answer 1

Here is an example:

F=ma or Force equals mass times acceleration (Newton)

A rocket's mass decreases as fuel is burned while the force of the burning fuel stays approximately the same. Knowing the "burn rate" (pounds per second) one can use calculus to determine the acceleration at any time during the burn.

Another example:

Buckets are truncated cones. Hoses put out water at a constant rate. The depth of the water increases the fastest where the diameter of the bucket is smallest and the slowest where the diameter is the largest. Calculus can be used to determine the change in depth at any moment during the filling process.

Answer 2

Consider a farmer who has 20 panels of fence, and wishes to make a square pen with the largest area possible for his sheep.

Set out the problem algebraically:

x + y = 20... (1)
A = x * y... (2) where A is the area, and x, y are the lengths.

Lets also assume x > y, so x is the longer of the lengths. This way we won't get two solutions (that are essentially the same), just one.

From (1), we can say that y = 20 - x, and we can substitute this in to (2).

=> A = x * (x - 20)
=> A = x^2 - 20x

Differentiating:

dA/dx = 2x - 20

We know that to find maxima or minima we must set dA/dx to zero: (this is where the graph would have a gradient of zero - i.e. be a peak or a trough - a maximum point or a minimum)

0 = 2x - 20

=> 2x = 20
=> x = 10

and from (1)

=> y = 10.

So the maximum area of the pen will be when x = 10 and y = 10.

This is a practical, yet admittedly application of calculus.

Answer 3

I used calculus to measure the heating oil left in my oil tank. The tank is cylindrical and in the ground horizontally (axis is horizontal. I integrated rectangles to give an equation for volume versus oil depth. I've used that calculation for many years.

As an engineer, I used calculus all the time in my work. It's a way to sharpen the mind (because it encourages a certain way of thinking about it) as well as a way to get answers. Certain physical exercises work with specific muscles. Calculus exercises specific areas of the brain.

Answer 4

If you take a collge entrance exam you could plot the test scores vs the frequency. It would look like a bell or normal curve. The average score would be near the middle of the curve. An equation would define the line. Then to determine different standard deviations, say one +/- std dev, you would need to integrate the area under the curve to determine what two points left and right of the middle value would give you a std dev, or 67% of the total area.

Answer 5

Calculus is used extensively in science and engineering.
Without it, you wouldn't be living in a city with all the modern day convenience. You would not be going to places in cars, on roads and bridges built using calculus. You would not have electricity at home, so no internet, no TV to watch. You won't have a refrigerator and have to go out to hunt bugs to find food!

Answer 6

Statistics use calculus.
There are many different trends in economics that are modeled with calculus.
Design of buildings, cars, aircraft.
Any sort of maximization or minimization problem uses calculus.

Answer 7

Newton's Law of cooling

dT/dt = -kT

which means that the rate a liquid cools down is proportional to its temperature. This can be used for heat transfer