Evaluate the following limit:
lim x --> 2 sqrt(x^2 - x)/(2x - 3)
Just plug in x=2 and evaluate the fraction.
sqrt(4-2)/(4-3) = sqrt 2
I assume that 2 is the limit of x, and not a coefficient of sqrt(x^2 -x)
You wrote it in a confusing manner
To evaluate the given limit, we will first try to evaluate the expression directly at x = 2. However, we notice that when x = 2, the denominator of the expression becomes 2(2) - 3 = 1, which would result in an undefined value.
In order to overcome this issue, we can simplify the expression in a way that cancels out the problematic term. Here's how we can do it:
Step 1: Simplifying the expression:
sqrt(x^2 - x)/(2x - 3) = sqrt(x(x - 1))/(2x - 3)
Step 2: Factoring out the common term:
sqrt(x(x - 1))/(2x - 3) = sqrt(x(x - 1))/(2(x - 1))
Step 3: Canceling out the common factor (x - 1):
sqrt(x(x - 1))/(2(x - 1)) = sqrt(x)/2
Step 4: Evaluating the limit:
lim x --> 2 sqrt(x)/2 = sqrt(2)/2
Therefore, the limit of the given expression as x approaches 2 is sqrt(2)/2.