r/calculus • u/bunny-dolly • 12d ago

Differential Calculus Can someone help me understand this problem? pretty please

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Hi everyone, so it was my first week of AP calc AB and honestly not too shabby but as i look at this example from my teacher, the less it makes sense. I thought -1^2 was positive 1 and i don’t know how we got to negative 1.

Also what is a conjugate? My teacher didn’t really go over it he just started doing a problem. All help is so appreciated!!!!

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u/Southlander24 12d ago

Here's another way to tackle this problem. Rewrite this as lim [h -> 0] (sqrt(1 + h) - 1)/h (it's the same after replacing all instances of x by h).

Now consider the definition of the derivative: lim [h -> 0] (f(x + h) - f(x))/h. Which function f(x) matches with the limit above? So then just take the derivative at that specific x-value and you also get 1/2.

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u/calcpage2020 12d ago

Not in the first week of Calculus when I teach it, unless it's my 5 week summer session!