Find the limit.
lim 5-x/(x^2-25)
x-->5
Here is the work I have so far:
lim 5-x/(x^2-25) = lim 5-x/(x-5)(x+5)
x-->5 x-->5
lim (1/x+5) = lim 1/10
x-->5 x-->5
I just wanted to double check with someone and see if the answer is supposed to be positive or negative. For the lim The answer I received is
x-->5 positive 1/10
Please confirm with me if this answer is correct! Thank you!
To find the limit, you correctly factored the expression by using the difference of squares formula. However, there seems to be a small mistake in the simplification step.
Starting with lim (5-x)/(x^2-25), you factored the denominator correctly as (x-5)(x+5). However, in the next step, you have written lim (1/x+5) instead of lim (1/(x-5)(x+5)).
To simplify the expression correctly, you need to rewrite it as:
lim (5 - x)/(x^2-25) = lim -1/(x-5)(x+5)
Now, evaluating the limit as x approaches 5:
lim -1/(x-5)(x+5) = -1/(5-5)(5+5) = -1/(0)(10) = undefined
Therefore, the limit does not exist since it approaches infinity as x approaches 5.
In conclusion, the answer is not positive or negative 1/10, but instead, the limit does not exist.