how do you solve
Lim sqrt((x+1)/(4(x-1))
x-infinity
To find the limit of the given expression as x approaches negative infinity, you need to simplify the expression and then evaluate the limit.
Let's first simplify the expression sqrt((x+1)/(4(x-1)).
1. Multiply the numerator and denominator by 1/x. This step helps us get rid of the square root in the expression:
sqrt((x+1)/(4(x-1))) × (1/x)/(1/x)
This simplifies to:
sqrt((1 + 1/x)/(4(x-1)/x)).
2. Simplify further:
= sqrt((1 + 1/x) / (4 - 4/x)).
3. As x approaches negative infinity, both 1/x and 4/x approach zero. Therefore, we can simplify the expression as follows:
= sqrt(1/4).
So, the answer is 1/2.
To summarize:
The limit of sqrt((x+1)/(4(x-1)) as x approaches negative infinity is 1/2.