Strange limit of a utility fonction
 
  
 
  
 
 
 
 
 
 
    
        
        asked 1 year ago  
 
 Cyrille gravatar image  
 
 
 
 
    
        
        updated 1 year ago  
 
 dan_fulea gravatar image  
 
 
 
 
 
According to my knowledge (and wikipedia) the utility fonction defined
 
var('x a b γ')
U_5 = lambda x, a, b, γ: ((1-γ)/γ)*(((a*x)/(1-γ))+b)^γ
 
is such that 
 
lim
 
but
 
limU = lim(U_5(x, 1, b, γ), γ=0)
show(LatexExpr(r"\lim_{\gamma\rightarrow 0}U_5(x, 1, b, γ) = "), limU)
 
returns \infty. Strange.  Should I commit an error  ?
 
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Comments
I have slightly edited the code, then put in in the right format, so that the post can be digested fluently. 
Let us use some letters that can be easily typed, and some special values for x,b:
sage: var('c');
sage: U_5(2, 1, 6, c)
-(c - 1)*(-2/(c - 1) + 6)^c/c
Let us now take the limit from this expression for c\to 0. Which is the limit? Why should it be \log 2?
(Wikipedia comes with easy links, maybe inserting the link would make the readers go there, and not guess for themselves which variable should be specialized to one to get a \log x-limit.)
dan_fulea gravatar imagedan_fulea (
    
        1 year ago
    )
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