The problem is lim --> 2 for g(x) which is 2((x-2/(squareroot x)-2)) I just substituted 2 in for x and 2((2-2)/(squareroot 2)-2) = 0 This doesn't look right. It seems like I'd need to try something different.

Can someone tell me if it's right or wrong? And if there's a different approach?

you are correct if that orig is correct.

are you certain the denominator is not

sqrt(x-2) That makes it a calculus problem.

No it only has the sqrt x. The -2 is outside of the sqrt.

Just so I know. Had it all been under the square root would I have multiplied the top and the bottom by that sqrt(x-2)?

I recall seeing this question posted several times and both MathMate and I both answered it.

I was going for a "search" to find solutions but was not successful.
I agree with bobpursley that there might be a typo here.

I used to teach basic limits this way:
Sub in the approach value into the expression
If you get:
1. a real value, then write down that value. You are done! next question!
2. if you get a/0, where a≠0, then the limit is unefined, or there is no limit
3. If you get 0/0, then you have a real Calculus limit question. Try factoring, rationalizing or some other fancy tricks you can think of.

in your case , sub in x = 2
expresssion = 2(0)/(√2 - 2) = 0/-.586 = 0

all done!

However, check your typing and make sure your brackets are in the right place.

the first 2 is centered on the division line which has x-2/(sqrt2)-2.

I think I placed the brackets right??

To determine whether your approach is correct or not, let's go through it step by step.

You want to find the limit of the function g(x) as x approaches 2. The function is given by g(x) = 2 * ((x - 2) / (√x - 2)).

First, you substituted 2 in for x, which gives you g(2) = 2 * ((2 - 2) / (√2 - 2)). Simplifying the numerator and denominator, you get g(2) = 2 * (0 / (0 - 2)). However, you encountered an issue with this approach.

The problem here is that you have an indeterminate form of 0/0. This means that the direct substitution is inconclusive and we need to try a different method to evaluate the limit.

One possible approach is to simplify the expression using algebraic manipulation or rationalization techniques:

g(x) = 2 * ((x - 2) / (√x - 2))

Multiply the numerator and denominator by the conjugate of the denominator to rationalize it:

g(x) = 2 * (x - 2) * (√x + 2) / ((√x - 2) * (√x + 2))

Now, expand and simplify the numerator:

g(x) = 2 * (x√x - 2√x + 2√x - 4) / (x - 4)

Simplify further:

g(x) = 2 * (x√x - 4) / (x - 4)

Now, we can attempt to evaluate the limit by direct substitution:

lim(x→2) g(x) = lim(x→2) 2 * (x√x - 4) / (x - 4)

Substituting x = 2 in the expression:

lim(x→2) g(x) = 2 * (2√2 - 4) / (2 - 4)
= 2 * (2√2 - 4) / (-2)
= -2√2 + 4

Therefore, the limit of g(x) as x approaches 2 is -2√2 + 4.

In summary, the direct substitution in your initial approach yielded an indeterminate form of 0/0. To find the limit, we need to simplify the expression and use rationalization techniques. The correct limit is -2√2 + 4.