The discussion revolves around finding the limit of the function f(x) = (x + 1)^(1/2) as h approaches 0, specifically focusing on the expression lim (f(x+h) - f(x))/h. Participants are exploring the implications of the limit leading to an indeterminate form.
The discussion is ongoing, with participants exploring different interpretations of the limit and considering various approaches to resolve the indeterminate form. Some guidance has been offered regarding the use of the conjugate, but no consensus has been reached.
There is a mention of the limit being of the [0/0] indeterminate form, which is a key point of discussion among participants. The original poster's repeated attempts indicate a focus on understanding the limit's behavior rather than arriving at a definitive answer.
No. This type of limit always is of the [0/0] indeterminate form.Prototype44 said:Homework Statement
lim f(x+h)-f(x)/h f(x)=(x+1)^(1/2) ans:1/2(x+1)^(1/2)
h→0
Homework Equations
The Attempt at a Solution
lim (x+h+1)^(1/2)-(x+1)^(1/2)/h lim (x+1)^(1/2)-(x+1)^(1/2)/h
h→0 h→0
Should the answer be D.N.E because the square roots cancel each other and leave 0/0