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why we use calculus

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9 years ago 419 Points
```							Dear Suyash
Differential calculus can be used for  finding the local slope and curvature of a function and important points  on a curve: maximum, minimum, inflection points, etc. These points  and  slopes can be the solution to a wide variety of problems related to  physics, mechanical and electrical design, perhaps chemistry and other  fields where a problem can be represented by an equation with variables.  One example, if you can derive total fuel consumption as a function of  acceleration there may be a minimum point of the function that allows  you to reach your target speed with the least fuel - this is especially  important with airplanes and rockets.  Integral calculus can be used to find the area under curves which can  represent the amount of work done, distance gone, energy exerted,  stress, angle and deflection of beams and a host of other scientific and  mechanical properties that can be characterized by equations.  One overly simple example: if I push on a 1 Kg rock in space with a  constant force of "A" newtons in the same direction where A represents a  constant.  The acceleration (a) as a function of time: a = A meters per second  squared. The graph will be a horizontal line with respect to time (t).  The speed (v for velocity) is the integral of the acceleration: v = A * t  + B where t is time (how many seconds) and B is the speed it was going  when we started. At+B is the integral of A with respect to time. The  graph will be a line sloping upward with slope of A units with respect  to t.  The distance traveled is the integral of the speed. One half A * t  squared + B * t + C where C is how far away it was when we started. (  .5At^2 + Bt + C) The graph will be a parabola with increasing slope with  respect to t.  Now, if a rocket starts with a mass of 60,000 Kg of which 50,000 is fuel  and uses 500 Kg of fuel per second and the force generated by the fuel  burn increases with altitude up to 15,000 m and decreases thereafter and  the air resistance goes up with speed and down with altitude, you will  need some calculus to determine how fast it will be going and how far it  has gone when it runs out of fuel.

All the best.
AKASH GOYAL

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9 years ago
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