Evaluate
lim x-->25
5 - square root x / x - 25
I don't get how the answer is -1/10
lim (5 - √x)/(x-25) as x ---> 25
= lim (5-√x)/((√x-5)(√x+5))
= lim -1/(√x+5) as x ---> 25
= -1/(5+5)
= -1/10
To evaluate the limit of the given expression, we can use direct substitution, which means substituting the value the variable is approaching (in this case, x = 25) into the expression and simplifying.
Let's substitute x = 25 into the expression:
5 - sqrt(25) / (25 - 25)
Since the square root of 25 is 5 and the denominator is 0, we have an indeterminate form of 0/0. This suggests that we need to simplify the expression further.
To do this, we can apply rationalization to the numerator:
5 - sqrt(25) = 5 - 5 = 0
Now, let's rewrite our expression:
0 / (25 - 25)
We still have 0/0, so further simplification is needed. Notice that the denominator is equal to zero. This indicates that we have a removable discontinuity, which means we can simplify the expression by canceling out the common factor of (x - 25) in both the numerator and the denominator.
Doing so, we have:
0 / 0 = 0
Therefore, the limit of the given expression as x approaches 25 is 0, not -1/10. It is important to double-check the answer for accuracy.