How do you find $lim (x+1)^(3/2)-x^(3/2)$ as $x->1^+$ ?

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Answer 1 · 2017-01-04T18:37:45

$2 sqrt 2 - 1$

$lim_(x to 1^+) (x+1)^(3/2)-x^(3/2)$

The function is continuous through x = 1 so you can just plug in the value x = 1 to get $2^(3/2) - 1 = sqrt 8 -1$

How do you find lim (x+1)^(3/2)-x^(3/2)lim (x+1)^(3/2)-x^(3/2) as x->1^+x->1^+?