What is lim x --> 1 [( 1- sqrt x)/ (1- x)]
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justaguide
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Now we see that ( 1- sqrt x)/ (1- x)
=> (1 – sqrt x)/(1- sqrt x)*(1+ sqrt x)
=> 1/ (1+ sqrt x)
For lim x --> 1 [( 1- sqrt x)/ (1- x)]
we have lim x --> 1 [1/ ( 1+ sqrt x)]
=> 1 / (1 + sqrt 1)
=> 1/ (1+1)
=> 1/2
Therefore lim x --> 1 [( 1- sqrt x)/ (1- x)] = 1/2
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giorgiana1976 | Student
We calculate the limit substituting x by 1
lim [( 1- sqrt x)/ (1- x)] = (1-1)/(1-1) = 0/0
We notice that we've get an indetermination case
We'll solve using L'Hospital rule:
lim [( 1- sqrt x)/ (1- x)] = lim ( 1- sqrt x)'/ (1- x)'
lim ( 1- sqrt x)'/ (1- x)' = lim (-1/2sqrtx)/-1
lim [( 1- sqrt x)/ (1- x)] = lim sqrt x/2
lim [( 1- sqrt x)/ (1- x)] = sqrt 1/2
lim [( 1- sqrt x)/ (1- x)] = 1/2
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