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The 'e' that keeps popping up in many math and engineering situations is the base of natural logarithms. It's an irrational number, meaning that it can never be exactly, precisely written with numerical digits. But if you'll settle for 15 decimal places, the value of 'e' is e = 2.7 1828 1828 45 90 45 (The spaces are there just to make it easier to read and memorize.)
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What are the practical applications of limits of function?
well derivatives cannt be used without limits so it is application for calculus
What is the connection between anti-derivatives and definite integrals?
Definite integrals are definite because the limits of integration are prescribed. It is also the area enclosed by the curve and the ordinates corresponding to the two limits of integration. Antiderivatives are inverse functios of derivatives. If the limits of the integral are dropped then the integration gives antiderivative. Example Definite integral of x with respect to x between the value of x squared divided by 2 between the limits 0 and 1 is 1/2. Antiderivative of x is x squared divided by two.
Why derivative is taken?
Derivatives are used to find instantaneous rate at which a function changes.
Why is calculus described as understanding something by looking at small pieces?
Both derivatives and integrals - two of the most important concepts in calculus - are defined in terms of limits; specifically, what happens when something gets smaller and smaller.
What is the use of a differential?
Differentials can be used to approximate a nonlinear function as a linear function. They can be used as a "factory" to quickly find partial derivatives. They can be used to test if a function is smooth.
