Υou show that it is continuous in every element of it's domain.
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A calculator can show a mortgage home buyer how quickly they can pay off their home and how much they save when they pay off the principal of the loan over a given time.
The different aspects of calculus are used in the real world every day. In business, specialists look at the derivatives of trends that can help them predict the future of stocks and markets. Architects commissioned for a job are given a budget and they use optimization to calculate the best amount of material they can get with that budget and space in a building they are designing. The Integral is used to show area under a curve. The indefinite integral is the antiderivative of a function. For these types of professions the integral is their Bible, metaphorically speaking. The watch the trends, convert the data into a quantitative function and then use the integral to predict the future of a company or simply use it with differentiation for an optimization problem. Their are many other uses as well that we use, sometimes subconsciously, in everyday life; these are just a couple of examples.
It is an abbreviation for 'flourished'. It is often used when the dates of birth and death are not known. For example, if dates for a composer were given as 'fl 1584-1602' it would show that there is documentary evidence that their work became best known during those years, but that there was no clear evidence of their birth and death.
You can compute that once you know specific values for variables x, and n. exp n is the exponential function, or antilog to base e. On scientific calculators, you would usually press keys like "inverse" "ln", or "shift" "ln", or something similar. To check whether you did the calculation correctly, exp 1 should show you approximately 2.718.
Not in its entirety.