Skip to main content

WHY CALCULUS

 

     Let us say, you are buying 10 chocolates for 20 dollars.  If you divide 20 by 10, you get 2.  So 2 dollar is the price of 1 chocolate.  Division always gives the rate.  In this case cost per unit.

      Another example:  a car covers 120 km in 2 hours.  120/2 = 60 km, It is the speed of the car.  Also rate of distance traveled by the car.  (distance traveled in one hour)

      In general Division y/x, gives the value of y when x is unity.

     Now let us assume that, we have two series as follows.

 x = 1,2,3,4,5,6....
y = 1,4,9,16,25,36...    = x^2

 Here, I want to find y/x.  But the values are not uniform and  they are growing.  What to do?  Here calculus comes to our help.

     It says, if y=x^2, then y/x or more correctly   dy/dx = 2x.

 Let us verify,
x = 3; y = 9
x  =4; y=16
For unit change in x(4-3=1), the change in y is 16 - 9 =7
The average of x = 3 and 4 is 3.5
So 2x=2*3.5 = 7
Hence, for unit change in x, the change in y is 2x - verified.

 For functions like, y =x^3, y = log(x) 
y=sin x and y = 3x+2x^2, the calculus gives us the division of dy/dx(differentiation) or the rate of change of y with respect to x.

 Using calculus, we can calculate, velocity, acceleration, inflation, current, voltage etc for continuously varying quantities.  

Comments

Post a Comment

Popular posts from this blog

Your heart -you do not know

  Size and Location: The human heart is roughly the size of a clenched fist and is located slightly to the left of the center of the chest. Despite its relatively small size, the heart plays a crucial role in pumping blood throughout the entire body. Heartbeat Variability: The heart does not beat at a constant rate. The interval between heartbeats can vary, and this variability is considered a sign of a healthy heart. Factors such as breathing, emotions, and physical activity influence the heartbeat. Electrical Conduction: The heart's contractions are controlled by electrical impulses. The sinoatrial (SA) node, often called the "natural pacemaker," generates electrical signals that regulate the heartbeat and coordinate the pumping of blood. Blood Pumping Capacity: On average, the human heart pumps about 2,000 gallons (or 7,570 liters) of blood each day. Over a lifetime, this amounts to pumping enough blood to fill several Olympic-sized swimming pools. Heart Chambers and V...
Post a Comment
Read more

THE WORK HORSE "="

    One cannot think of  a mathematical step without 'is equal to ' .  It balances right hand side and left hand side.  It aids simplification and manipulation of a mathematical expression. example: 2(A+B)  = C 2A+2B  = C         2A = C-2B           A = C-2B/ 2   In an electronic calculator,  the pressing of ' = " sign executes an asthmatic expression  or simply calculates.       In computer languages, it plays very important role.                                                                 A = B   When a computer looks at this expression, the value stored in the location named B is just transferred to the storage named A .  After execution both A and B will have the same value an...
Post a Comment
Read more

How does your smart phone detect motion, steps, rotation, and location?

 How it works-1  An accelerometer in a smartphone is a microelectromechanical system (MEMS) device that measures acceleration and tilt. It works by detecting changes in motion by measuring the vibration or acceleration of the device. The accelerometer consists of a small mass suspended on a spring inside a sealed chamber. When the device is subjected to acceleration, the mass moves relative to the device, causing a change in capacitance that can be measured and processed by the smartphone's hardware. The accelerometer measures acceleration in three dimensions (x, y, and z) and provides data that the smartphone's software can use to determine the device's orientation, detect motion, and track changes in velocity and acceleration. The accelerometer is used for a variety of purposes in a smartphone, including screen rotation, motion tracking for games and fitness apps, and detecting the position of the device for navigation and location services. Additionally, it can be used t...
Post a Comment
Read more