Question

assume \\(\lim_{x \to 4} f(x) = 20\\) and \\(\lim_{x \to 4} g(x) = 3\\). compute the following limit and state the limit laws used to justify the computation.

\\(\lim_{x \to 4} (f(x) - g(x))\\)

\\(\lim_{x \to 4} (f(x) - g(x)) = \\) (simplify your answer.)

select each limit law used to justify the computation.

a. root
b. squeeze theorem
c. difference
d. product
e. power
f. linear function
g. quotient

Explanation:

Apply the Difference Law for Limits

$$ \lim_{x \to 4} (f(x) - g(x)) = \lim_{x \to 4} f(x) - \lim_{x \to 4} g(x) $$

Substitute the given limit values

$$ \lim_{x \to 4} (f(x) - g(x)) = 20 - 3 = 17 $$

Identify the limit laws used

The only limit law applied to justify the computation is the Difference Law.

Answer:

Question 1

\(\lim_{x \to 4} (f(x) - g(x)) =\) <blank>17</blank>

Question 2

• A. Root
• B. Squeeze Theorem
• C. Difference (Correct answer)
• D. Product
• E. Power
• F. Linear Function
• G. Quotient