Unformatted text preview: 1 : If f ( x ) < g ( x ) for all x , then lim x → a f ( x ) < lim x → a g ( x ). 4. Prove or disprove: If lim x → a f ( x ) and lim x → a g ( x ) do not exist, then neither lim x → a ( f + g )( x ) exists nor the lim x → a ( fg )( x ) exists. 5. Give an example where lim x → a f ( x 2 ) exists but lim x → a f ( x ) does not. 6. Prove that lim x → a f ( x ) exists if lim x → a + f ( x ) = lim x → a-f ( x ) 1 Disproving is in general easier than proving: you just have to come up with one example in which the statement is false 1...
View Full Document
- Spring '10
- Electrical Engineering, Scientific evidence, University of Engineering and Technology Lahore Department of Electrical Engineering, Technology Lahore Department, x→a x→a