TN class 11 maths solutions ஒரே இடத்தில் உங்களுக்காக தருகின்றோம். students க்கு எந்தமாதிரி சொல்லிக்கொடுத்தால் புரியும் என்று நங்கள் ஆராய்ச்சி செய்து ஒரு புது முறையை உங்களுக்காக வழங்குகின்றோம்.

TN class 11 maths students க்கு எளிதில் புரியும் வகையில் maths solution ஐ நங்கள் board மூலம் தெளிவாக்குகின்றோம்.

உங்களுக்கு இந்த 11 maths guide புடித்திருந்தால் நீங்கள் உங்கள் நண்பர்களுக்கு இங்கு share செய்யலாம்.

The part of mathematics that deals with the ratio of change of quantities are called calculus. There are two kinds of calculus, one is pre-calculus and the other is calculus. Precalculus is mostly static and calculus is dynamic. For instance, pre-calculus deals with the slope of a line and the rate of speed of a constantly moving object. But calculus deals with the slope of a curve and the rate of speed of a changing speed object.

Calculus deals with the rate of change and has wide applications across physicists, chemists, economists, geologists, biologists, and psychologists. If you look at each of these professions, they will deal with a rate of change in their interest areas. For instance, the physicist deals with the velocity of the object and they will try to calculate the rate of change in velocity. The chemist deals with the rate of change from one substance to another substance. The biologist deals with the change of rate of the population of a species (i.e either animals or plants) over some time. The economist deal with the rate of change of the share price, economic indexes, CPIs...etc over some time. The geologist deals with the rate of change of decomposition of ancient objects to find out the real age of the old items excavated from the earth. Hence learning calculus is very important for students as it has applicability in any of the professional careers they would be taking over in their life.

The calculus was introduced by Sir Isaac Newton from England and Gottfried Wilhelm Leibnitz from Germany around the same time. The credit for creating the differential calculus goes to Newton, who after becoming an expert in mathematics he spent his time inventing new concepts related to the rate of change. This causes the birth of Calculus.

There is a conflict around who first discovered calculus - Newton or Leibnitz. Leibnitz published many of the journals related to calculus and was the first to create important results related to calculus. Another major mathematician who contributed to calculus is Augustine Louis Cauchy. He is the first mathematician who created the definition of a limit and created the formula for the limits of difference quotients.

Another major mathematician who contributed to calculus is Karl Weierstrass. He is a german mathematician who primarily gave the concepts of limits, differentiability and continuity.

To calculate the tangent to a circle we can use pre-calculus methods. But to analyse the tangent to a curve we need to use calculus. Similarly to analyse the area of a square we can use pre-calculus methods but to analyse the area under a curve we need to use the calculus methods.

Calculus has three stages. It starts with pre-calculus and then the limit process and then finally the calculus. Without knowing the definition it is not advisable for students to learn calculus as a set of formulas.

Even though calculus is around for 1000s of years, the concept of limit has been devised only during the 19th century by Louis and Karl.

If we take an example of a function y= x^2 + 5, then we can draw the points of y with respect to x. This will form a U shared curve above the origin which cuts through the y axis at 5.