Finding delta given epsilon for limit of 1/(2-x) as x approaches 5

[gefops]

Could you help me with the problem?

Find delta using the definition of limits, given epsilon = 0,25

lim 1 / (2-x) = -1/3
x->5

Answer should be delta = 1
How can I get it?

Thanks.

 

[willem2]

Apply the definition of limits to

lim 1 / (2-x) = -1/3
x->5

 

[Landau]

Note that there is not just one correct answer. If some delta works, then any smaller one (>0) also works.

 

[sponsoredwalk]

You musn't have understood the book or whatever you used to learn about the formal definition of the limit.

I can't go crazily deep into it but I'm sure my links will help you understand the idea behind it.

http://www.5min.com/Video/The-Formal-Definition-of-a-Limit-169078903

This link will give you an idea of the general idea.

http://www.youtube.com/watch?v=-ejyeII0i5c&feature=youtube_gdata

This video (and the one following it in the playlist) give some examples on applying it.

http://docs.google.com/viewer?a=v&q=cache:_OYvmsulbDIJ:www.ocf.berkeley.edu/~yosenl/math/epsilon-delta.pdf+epsilon-delta+limit+example&hl=en&sig=AHIEtbQijZifL9dG46lTjmQMCpKpcrrY1g

This pdf is also very useful.

Personally, most of the places I've seen this version of the limit discussed have always left me in the dark, shameful authors, this idea is so simple & intuitive idk why they can't explain it properly.