MATH138 Lecture Notes - Monotonic Function, Limit Of A Sequence, Pythagorean Theorem

• School: University of Waterloo
• Department: Mathematics
• Course: MATH138
• Professor: Rui Bin Qin

Document Summary

, then ( ) ( ), where f is antiderivatives of f, i. e. f" = f ( ) ( ), where a is an arbitrary constant. If u = g(x) is differentiable and its range i is the domain of a continuous function f, then. Let u = f(x), v = g(x), then . Improper rational functions: is improper if ( ) ( ), where ( ) Definition: let s is a solid between a and b. If the cross sectional area of s is a(x) (continuous), then volume of s is ( (riemann sum) Using pythagorean theorem, y is given by . Therefore the area of the cross-sectional area a is given by. Divide s into n pieces of equal width by using the planes where the planes are perpendicular to x-axis and in through . [ ], then we can approximate the i-th. Adding volumes of these slice by ( slices, then we will get ( )