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Frigus
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My question is as it is as you have read in the heading and please tell me in taking mind that I am not a calculus master but just a beginner.
Sir I understand it but I was watching this mit lecture in which that sir told (at 0:30)that we write it as positive because this is how we define differential but it didn't made any sense to me so to clarify it I posted this thread.PeroK said:If ##dM## is a negative quantity, as Resnick states, then ##M + dM## is correct.
E.g. suppose ##M = 100kg## and ##dM = -1 kg##, then the new mass is:
##M' = M + dM = 100kg + (-1kg) = 99kg##
Hemant said:Sir I understand it but I was watching this mit lecture in which that sir told (at 0:30)that we write it as positive because this is how we define differential but it didn't made any sense to me so to clarify it I posted this thread.
Can you please explain the point that he wanted to explain.
Calculus is a branch of mathematics that deals with the study of change and motion. It involves the use of mathematical methods to analyze and model continuous change in quantities such as speed, acceleration, and area.
Calculus is important because it provides powerful tools for solving real-world problems in various fields such as physics, engineering, economics, and statistics. It also helps in understanding the fundamental concepts of mathematics and provides a foundation for more advanced topics.
The two main branches of calculus are differential calculus and integral calculus. Differential calculus deals with the study of rates of change and slopes, while integral calculus deals with the accumulation of quantities and finding the area under curves.
The basic concepts in calculus include limits, derivatives, and integrals. Limits are used to define the behavior of a function at a specific point, derivatives are used to find the rate of change of a function, and integrals are used to find the area under a curve.
Calculus has numerous applications in real life, such as in engineering for designing structures and predicting motion, in economics for analyzing markets and optimizing profits, and in medicine for modeling biological processes. It is also used in everyday situations, such as calculating rates of change and finding optimal solutions.