# Need help trying to do basic limit

## Homework Statement

lim
$$_{}h\rightarrow0$$ ($$\sqrt{a+h}$$ - $$\sqrt{a}$$) / h

3. ok so i multiplied by $$\sqrt{a+h}$$ + $$\sqrt{a}$$. The top simplified to a+ h -a, aka h. the bottom is h($$\sqrt{a+h}$$ + $$\sqrt{a}$$).

The h cancels, so I am left with

1 / ($$\sqrt{a+h}$$ + $$\sqrt{a}$$

how do i simplify this further?

thanks!

jgens
Gold Member
No need to simplify any further, just note what happens as $h \to 0$.

Supposedly I can simplify it to

1
----
2$$\sqrt{a}$$?

jgens
Gold Member
Which is what you get when you evaluate the limit as $h \to 0$.

It makes perfect sense as well that that is your answer. I am not sure of the extent of your understanding of differentiation, however, if you know enough, you should be able to recall that the derivative of a^(1/2) = 1/2a^(1/2) which is exactly what you got.

Mark44
Mentor
It makes perfect sense as well that that is your answer. I am not sure of the extent of your understanding of differentiation, however, if you know enough, you should be able to recall that the derivative of a^(1/2) = 1/2a^(1/2) which is exactly what you got.

A clearer way of writing this would be a^(1/2) = 1/(2a^(1/2)). A literal reading of what you wrote would be 1/2*a^(1/2); that is, the fractional power would be in the numerator, which I'm sure you didn't intend.