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If f is defined by the function f(x)=x-4/x-2 then lim f(x) is equivalent to which of the following

If f is defined by the function f(x)=x-4/x-2 then lim f(x) is equivalent to which-example-1
User CCPony
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1.9k points

1 Answer

4 votes
4 votes

Answer:

The correct answer is the third option:


\lim_(x\to4)(√(x)-2)

Step-by-step explanation:

We have the function:


f(x)=(x-4)/(√(x)-2)

In the numerator, we have x - 4. We can rewrite it as a difference of squares, since:


\begin{gathered} x=(√(x))^2 \\ 4=2^2 \end{gathered}

Thus:


x-4=(√(x)-2)(√(x)+2)

Then, the limit:


\begin{gathered} \lim_(x\to4)(((√(x)-2)(√(x)+2))/((√(x)-2)) \\ \end{gathered}

We can cancel out the terms, since we are taking limit, this is, numbers that infinitely close to 4, bt never 4. This way we can cancel the terms, and get:


\lim_(x\to4)(√(x)+2)

User Willem Van Rumpt
by
3.0k points
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