1. ## limit and functions

Hi

I would like some help for my homework:

Ex1:

Consider un function f which is defined by

f(x) = (square root (x+1)) - 1
___________________
(square root (x+2)) - 2

(I can't find square root sign, so I wrote it)

Give it's domain of definition and calculate it's limit when it's 0

Thank you very much

2. Originally Posted by french
Hi

I would like some help for my homework:

Ex1:

Consider un function f which is defined by

f(x) = (square root (x+1)) - 1
___________________
(square root (x+2)) - 2

(I can't find square root sign, so I wrote it)

Give it's domain of definition
of course, since this is homework, we cannot do the problem for you. here's what you need to know

the domain of an expression is the set of all input values (usually, and in this case, x-values) for which the function is defined. that is, what values can we plug in and actually get an answer.

it is often easier to find the values which do not work, and say the domain is all values but those values.

useful facts: rational functions, that is, functions that look like fractions are defined wherever the denominator is not zero. that is, the domain of a real function $\frac {f(x)}{g(x)}$ is all real x such that $g(x) \ne 0$. there are several different notations in which you can express the domain. you should know what your professor requires.

squareroot functions are defined where what is squarerooted is greater than or equal to zero. that is, the domain of the function $\sqrt{f(x)}$ is all real x such that $f(x) \ge 0$

put those two together to find the domain of the given expression

and calculate it's limit when it's 0
do you mean to find the limit as $x \to 0$? question: is x = 0 in the domain of the function? how do we find the limit if this is the case? what if i asked you to find $\lim_{x \to 0} (x + 1)$, what would you do?