Question

My math teacher has the answer as -1/4. I got 1/4 and cannot figure out the negative part.

Answer 1

To find the limit we need to rationalize the function, we achieve this by multiplying by a one written in an appropiate way:

`\begin{gathered} \lim_(h\to0)(2-√(4+h))/(h)=\lim_(h\to0)(2-√(4+h))/(h)\cdot(2+√(4+h))/(2+√(4+h)) \\ =\lim_(h\to0)((4-(√(4+h))^2))/(h(2+√(4+h))) \\ =\lim_(h\to0)(4-(4+h))/(h(2+√(4+h))) \\ =\lim_(h\to0)(4-4-h)/(h(2+√(4+h))) \\ =\lim_(h\to0)(-h)/(h(2+√(4+h))) \\ =\lim_(h\to0)(-1)/(2+√(4+h)) \\ =-(1)/(2+√(4+0)) \\ =-(1)/(2+√(4)) \\ =-(1)/(2+2) \\ =-(1)/(4) \end{gathered}`

Therefore:

`\lim_(h\to0)(2-√(4+h))/(h)=-(1)/(4)`