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?
To determine if your solution is right or wrong, we need to analyze your approach.
First, let's look at the original expression: g(x) = 2((x-2)/(√x-2)).
You substituted x = 2 into the expression, which is a good starting point. However, your evaluation seems to be incorrect. Let's go through the steps again:
g(2) = 2((2-2)/(√2-2)).
Now let's simplify the numerator and denominator separately:
Numerator: (2-2) = 0.
Denominator: √2-2 is the difference between the square root of 2 and 2.
At this point, we have 0/√2-2.
However, dividing by √2-2 directly would result in division by zero, which is undefined.
To solve this problem correctly, you can try a different approach. One common method is to simplify the expression, either by algebraic manipulation or invoking limit laws, so that you can substitute the value directly without encountering any undefined behavior.
In this case, we can simplify the expression by rationalizing the denominator. By multiplying the numerator and denominator by the conjugate of the denominator, we can eliminate the square root:
g(x) = 2((x-2)/(√x-2)) * (√x+2)/(√x+2)
= 2(x-2)/(x-2)
= 2.
Now, as x approaches 2, g(x) approaches 2. So the correct answer should be g(2) = 2.
In summary, your initial approach had an error in evaluating the expression. By simplifying the expression and rationalizing the denominator, you will be able to determine the limit correctly.