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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

Best Answer 

 #1
avatar+4384 
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\(\lim \limits_{x \to 9} \left(3f(x) + f(x)g(x)\right) = 27\\ 3 \lim \limits_{x \to 9} f(x) + \lim \limits_{x \to 9} f(x)g(x) = 27\\ 3 \lim \limits_{x \to 9} f(x) + g(9) \lim \limits_{x \to 9} f(x) = 27\\ 3 \lim \limits_{x \to 9} f(x) +6 \lim \limits_{x \to 9} f(x) = 27\\ 9 \lim \limits_{x \to 9} f(x) = 27\\ \lim \limits_{x \to 9} f(x) = 3 \\ f \text{ is given to be continuous so }\\ f(9) = \lim \limits_{x \to 9} f(x) = 3\)

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 Feb 6, 2019
 #1
avatar+4384 
+1
Best Answer

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

Rom Feb 6, 2019

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