In my university, the first calculus course for most of the people uses only an intuitive definition of limit (without epsilon/delta or epsilon/n_0). Also the definition of derivative and integral is intuitive. The idea is that the students can do the calculations following some rules. And then see some applications, like the tangent line of a function or the area below a function.
The first calculus course for engineers and exact science students is more difficult, but the discussion of the technical details of the limit is very small. Perhaps calculate the limit by definition only for 2 or 3 easy functions, and then just use the algebraic properties of the limit.
The second course for Math and Physics students has more time assigned to the calculation of limits by definition.
The first calculus course for engineers and exact science students is more difficult, but the discussion of the technical details of the limit is very small. Perhaps calculate the limit by definition only for 2 or 3 easy functions, and then just use the algebraic properties of the limit.
The second course for Math and Physics students has more time assigned to the calculation of limits by definition.