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I have a question about problem 53 on page 64. I graphed the function and found the limit (I got 0), but I don't know how to prove it using the Sandwich Theorem. I know that if two functions have the same limit then the third function will also have that limit but I don't know how to find the other two functions. All I have is the xsin(x) part. Do you just chose any two functions that have the limit of 0 as x approaches 0? I chose x and x^2 so my inequality looked like lim x< lim xsin(x) < lim x^2. Is that right?
ReplyDeleteThanks,
Katie W
To use the Sandwich Theorem, you need: 1) two functions with the same limit at the given x value (so if you were to show the limit as x approaches 7 is 100, you want two functions who have limits of 100 as x approaches 7) and, 2) a function that is less than or equal to the given function throughout an interval around the chosen x value and a function that is greater than or equal to your given function throughout the same interval.
ReplyDeleteSome helpful advice on using the sandwich theorem, try to use a constant function for one of the bounding functions, such as f(x) = 0.
For #53, choose an interval about x = 0 (it can be as large or small as you wish). Is it true that x <= xsinx <= x^2 on this ENTIRE interval? If so, then you're good. If not, choose different bounding function(s).
~Coach Wilson
~Coach Wilson
After you fill the holes in number 4a on the turn-in is the function then continuous from negative infinity to infinity?
ReplyDeleteThanks,
Rachel Hersch
That makes sense since we took out the discontinuities.
Delete-Allison Honet-
Are you suppose to use IVT for number 2 in the turn in? Did anyone else use this in their explanation of why they chose their k value?
ReplyDeleteLaura G.
Number 2 is an existence question ("show something exists"). We only have one way/theorem so far for this case, so I think you're on the right track. Try breaking the interval into two parts so you have two separate IVT questions...
DeleteCoach Wilson
Test --- Coach Wi8lson
ReplyDelete