Help with limit question: lim_{h->0} 1/((x+h)^2 + a) - 1/(x^2 + a), a > 0

[matheyyy]

Hi all,

How do you go about solving this? I've got a feeling it requires some Algerba first to simplify but don't know where to start.

Thanks.

 

[stapel]

How do you go about solving this? I've got a feeling it requires some Algerba first to simplify but don't know where to start.

The numerator is a difference of fractions:

[imath]\qquad \lim\limits_{h \rarr 0} \; \dfrac{\dfrac{1}{(x+h)^2 + a} - \dfrac{1}{x^2 + a}}{h}[/imath]

Start in the usual manner: Find a common denominator, combine, and simplify.

Eliz.

 

[Steven G]

Have you learned about derivatives yet? If so, does this limit look like a derivative of some function?
BTW, Algebra is an important prerequisite for Calculus.