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Difference between integral and differential calculus?
Differential calculus is concerned with finding the slope of a curve at different points. Integral calculus is concerned with finding the area under a curve.
Why is calculus so interesting?
Because calculus applications are almost infinite. In fact, every branch of science uses calculus : physics, chemistry, biology, social studies, economics, etc. Calculus is a universal language that can be used to answer bunches of questions. Using calculus, you can solve various problems including the acceleration of planets in orbit, the kinetic energy of a car in motion, the equivalence point of a chemical reaction, the maximal profit a business can make, the lenght of any curved figure or the area and volume of eccentrical shapes, the electric field produced by a charged object, ... Calculus is interesting because you can use it everywhere!
How would you calculus surface area to volume ratio?
The answer will depend on shape in question.
How is calculus used in physics?
Physics is an especially heavy user of the calculus: mechanics, electromagnetism, acoustics, optics. Richard Feynman was known for his great facility in this area of mathematics.
Why does calculus work?
becasue it was designed cleverly and the area of a rectange is width times height
