+0

# Calculus

+1
298
1
+322

Suppose f and g are continuous functions such that

g(9) = 6 and lim x → 9 [3f(x) + f(x)g(x)] = 27.

Find f(9).

Feb 6, 2019

#1
+6196
+1

$$\lim \limits_{x \to 9} \left(3f(x) + f(x)g(x)\right) = 27\\ 3 \lim \limits_{x \to 9} f(x) + \lim \limits_{x \to 9} f(x)g(x) = 27\\ 3 \lim \limits_{x \to 9} f(x) + g(9) \lim \limits_{x \to 9} f(x) = 27\\ 3 \lim \limits_{x \to 9} f(x) +6 \lim \limits_{x \to 9} f(x) = 27\\ 9 \lim \limits_{x \to 9} f(x) = 27\\ \lim \limits_{x \to 9} f(x) = 3 \\ f \text{ is given to be continuous so }\\ f(9) = \lim \limits_{x \to 9} f(x) = 3$$

.
Feb 6, 2019

$$\lim \limits_{x \to 9} \left(3f(x) + f(x)g(x)\right) = 27\\ 3 \lim \limits_{x \to 9} f(x) + \lim \limits_{x \to 9} f(x)g(x) = 27\\ 3 \lim \limits_{x \to 9} f(x) + g(9) \lim \limits_{x \to 9} f(x) = 27\\ 3 \lim \limits_{x \to 9} f(x) +6 \lim \limits_{x \to 9} f(x) = 27\\ 9 \lim \limits_{x \to 9} f(x) = 27\\ \lim \limits_{x \to 9} f(x) = 3 \\ f \text{ is given to be continuous so }\\ f(9) = \lim \limits_{x \to 9} f(x) = 3$$