lim as x approaches 3+
x^2+x-6/18-3x-x^2
I factored it into (x+3)(x-2)/(6+x)(3-x)
lim does not exist, tends to - inf
Thank you. I understand that it's because of the (3-x) on bottom that makes it negative?
To find the limit as x approaches 3+ of the given expression, let's simplify it using the factored form you obtained:
(x^2 + x - 6) / (18 - 3x - x^2)
= [(x + 3)(x - 2)] / [(6 + x)(3 - x)]
Now, to find the limit, we substitute the value of 3 into the expression:
[(3 + 3)(3 - 2)] / [(6 + 3)(3 - 3)]
= (6)(1) / (9)(0)
At this point, we can see that the denominator is zero, which means that the expression is undefined at x = 3. In other words, there is no limit as x approaches 3 from the positive side.
Therefore, the limit as x approaches 3+ of the given expression does not exist.