Find the following limit or state that it does not...

Find the following limit or state that it does not exist.\\ \(\lim_{x \to -5} \frac{4(2x + 3)^2 - 196}{x + 5}\) Simplify the given limit. \(\lim_{x \to -5} \frac{4(2x + 3)^2 - 196}{x + 5} = \lim_{x \to -5} \boxed{}\) (Simplify your answer.)

Transcript

00:01 Okay, so let's get started with the first limit.

00:05 Limit as x goes to 7 of x squared plus 4x over x squared minus 3x minus 28.

00:21 Perfect.

00:22 Now let's keep in mind that the numerator here evaluated that x equal to 7 is different from 0.

00:30 The denominator evaluated at x equal to 7 is equal to what? well, we're going to have 7 squared minus 21, minus 28, and well, this one is equal to 0.

00:44 So this limit here does not exist, does not exist because the numerator is not equal to 0, does not go to 0 as x goes to 7.

01:00 Perfect.

01:02 Now, to be very precise, let's just notice that even though the two -sided limit does not exist, we can still compute the left limit and the right limit.

01:20 More precisely, limit as x goes to 7 from the left of x squared plus 4.

01:30 X over x squared minus 3x minus 28 well this limit here is equal to negative infinity because as x goes to 7 from the left this guy here goes to 0 from the left so from negative values and limit as x goes to 7 from the right of x squared plus 4 x over x minus 3x minus 28 well this guy is equal to positive infinity because this guy goes to 0 goes to 0 from the right that is true positive values okay perfect now let's compute our second limit well the second limit here is limit as x goes to 2 of 2 minus x over x over x plus 2.

02:38 Well, this limit here is clearly equal to 0, is clearly equal to 0 because this guy goes to 0 as x goes to 2, this guy goes to 4...

Question

Find the following limit or state that it does not exist.\\ \(\lim_{x \to -5} \frac{4(2x + 3)^2 - 196}{x + 5}\) Simplify the given limit. \(\lim_{x \to -5} \frac{4(2x + 3)^2 - 196}{x + 5} = \lim_{x \to -5} \boxed{}\) (Simplify your answer.)

Please give Ace some feedback