Ap Calc question.

[MasonJar]

I don't know if this belongs in this calc board, or the other, but here it is.

if f(x) = (sqrt(2x+5)-sqrt(x+7)) / (x-2) for x ? 2, and if f is continuous at x = 2, then k = ?
f(2) = k

Sorry, I don't know how to do the symbols, so I had to type it out like this. sqrt = square root.

I also need to know how you do it, not just the answer.

Thanks in advance for any help. I really appreciate it.

 

[Deleted member 4993]

I don't know if this belongs in this calc board, or the other, but here it is.

if f(x) = (sqrt(2x+5)-sqrt(x+7)) / (x-2) for x ? 2, and if f is continuous at x = 2, then k = ?
f(2) = k

Sorry, I don't know how to do the symbols, so I had to type it out like this. sqrt = square root.

I also need to know how you do it, not just the answer.

Thanks in advance for any help. I really appreciate it.

What is the requirement for the function to be continuous at x=2?

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[MasonJar]

Honestly I have no idea where to start with this problem. I'm not good with Calculus, at all.

 

[galactus]

Try finding the limit as x approaches 2.

\(\displaystyle \lim_{x\to 2}\frac{\sqrt{2x+5}-\sqrt{x+7}}{x-2}\)........[1]

Multiply top and bottom by the conjugate of the numerator to whittle it down.

Then, you can sub in x=2 and find the limit.

the problem says it is continuous at x=2. Graph it and you can see.

The defintion of continuity says that f(c) is defined. In this case, f(2) is defined.

\(\displaystyle \lim_{x\to c}f(x)\) exists. That is, the limit exists.

\(\displaystyle \lim_{x\to c}f(x)=f(c)\). In this case, \(\displaystyle \lim_{x\to 2}f(x)=f(2)\)

So, try finding the limit in [1].