Question

use \\(\lim_{x \to c} f(x) = -6\\) and \\(\lim_{x \to c} g(x) = -5\\) to find the limit.

\\\lim_{x \to c} 5f(x) - 2g(x)\\

Explanation:

Apply limit laws to decompose the expression

$$ \lim_{x \to c} [5f(x) - 2g(x)] = \lim_{x \to c} [5f(x)] - \lim_{x \to c} [2g(x)] = 5\lim_{x \to c} f(x) - 2\lim_{x \to c} g(x) $$

Substitute the given limit values

$$ 5(-6) - 2(-5) $$

Simplify the numerical expression

$$ -30 + 10 = -20 $$

Answer:

Use \(\lim_{x \to c} f(x) = -6\) and \(\lim_{x \to c} g(x) = -5\) to find the limit.

$$\lim_{x \to c} [5f(x) - 2g(x)] =$$

<blank>\(-20\)</blank>