Evaluate limx→43−x+5−−−−√x−4

To evaluate the given limit, we can start by substituting the value of x into the expression.

limx→43−x+5−−−−√x−4

Substituting x = 4 into the expression, we get:

limx→43−4+5−−−−√4−4

Simplifying further, we have:

limx→43−4+5−−−−√0

Since the square root of 0 is 0, we can simplify the expression to:

limx→43−4+5−−−−0

Next, we can simplify the numerator:

43−4+5 = 44+5 = 49

Now, we have:

limx→49−−−−0

Since the denominator is 0, we cannot directly evaluate the limit. However, we can use the concept of one-sided limits to determine the value.

To find the left-hand limit, we approach x from values less than 49. Let's substitute x = 48 into the expression:

limx→48−−−−0

Simplifying, we have:

48−4+5−−−−0 = 49−−−−0 = 49

Therefore, the left-hand limit is 49.

To find the right-hand limit, we approach x from values greater than 49. Let's substitute x = 50 into the expression:

limx→50−−−−0

Simplifying, we have:

50−4+5−−−−0 = 51−−−−0 = 51

Therefore, the right-hand limit is 51.

Since the left-hand limit and the right-hand limit are different, the overall limit does not exist.

Hence, the evaluation of the given limit limx→43−x+5−−−−√x−4 is "does not exist".