Evaluate the following limits
(x^2 + 2x - 8)/x-2
Lim x->2
To evaluate the limit as x approaches 2, we can try direct substitution by plugging in the value of 2 into the given expression:
(2^2 + 2(2) - 8) / (2 - 2)
Simplifying further:
(4 + 4 - 8) / 0
We observe that we have a denominator of 0. Division by 0 is undefined in mathematics, so we can't directly evaluate the limit using substitution in this case.
However, we can try to simplify the expression further by factoring and canceling any common factors. Let's factor the numerator:
(2x - 4)(x + 2) / (x - 2)
Now we can cancel out the common factor of (x - 2):
(x + 2) / 1
Simplifying further, we get:
x + 2
Now we can substitute the value of x into this simplified expression:
2 + 2 = 4
Therefore, the limit as x approaches 2 is equal to 4.