Evaluate the following limit
lim
x--> 2
Square root over x^2 - x/2x - 3
In this case, you can just plug in 2 for x to get the limit. The denominator remains finite
To evaluate the given limit, we can use direct substitution. Substitute the value x = 2 into the expression:
lim
x--> 2
√(x^2 - x)/(2x - 3)
Now, substitute x = 2 into the expression:
√((2)^2 - 2)/(2(2) - 3)
Simplifying further:
√(4 - 2)/(4 - 3)
√(2)/(1)
Taking the square root of 2 gives:
√2/1
Therefore, the value of the limit as x approaches 2 is √2/1, or simply √2.