MAT135H1 Lecture Notes - Lecture 3: Squeeze Theorem, Function Composition, Phenomenon

• School: UTSG
• Department: Mathematics
• Course: MAT135H1
• Professor: natalia Christina Garcia

Document Summary

Mat135h1 f - lecture 3 - calculus 1(a) Example 1: apply squeeze theorem to lim x 0 x 2 cos. ) = 0 = lim x 0 x 2( By te squeeze theorem, lim x 0 x 2 cos. Example 2: let 2 g x( ) 5 for all x. Find lim x g x( ) x 3 + 5. 2 g x( ) 5 using squeeze theorem. As x approaches infinity, x 3 + 5 x 3 + 5. 0 g x( ) x 3 + 5 g x( ) x 3 + 5. Use language of limits to define continuous functions. A function is continuous at the point c r if lim x c f x( ) = f lim x c x. If the function is continuous at all points in r, we say that it is a continuous function i. e. not only does the limit exist, it is exactly equal to f c( )