Question

1 multiple choice 1 point
for the following limit, if it exists.
\\(\lim\limits_{x\to 5} \frac{x^2 + 25}{x + 5}\\)
\\(\bigcirc\\) 5
\\(\bigcirc\\) 10
\\(\bigcirc\\) 0
\\(\bigcirc\\) does not exist
2 multiple choice 1 point
for the following limit, if it exists.
\\(\lim\limits_{x\to -4} \frac{x^2 - 16}{x + 4}\\)
\\(\bigcirc\\) -4
\\(\bigcirc\\) 1
\\(\bigcirc\\) -8
\\(\bigcirc\\) does not exist

Explanation:

Question 1

Step1: Substitute \( x = 5 \)

Substitute \( x = 5 \) into \( \frac{x^2 + 25}{x + 5} \), we get \( \frac{5^2 + 25}{5 + 5}=\frac{25 + 25}{10}=\frac{50}{10} = 5 \).

Step1: Factor the numerator

Factor \( x^2 - 16 \) as \( (x - 4)(x + 4) \), so the expression becomes \( \frac{(x - 4)(x + 4)}{x + 4} \).

Step2: Cancel common factor

Cancel \( x + 4 \) (for \( x
eq - 4 \)), we get \( x - 4 \).

Step3: Substitute \( x=-4 \)

Substitute \( x = - 4 \) into \( x - 4 \), we get \( -4-4=-8 \).

Answer:

5

Question 2