terem5
Answered

Suppose f and g are continuous functions such that

g(9) = 2

and

lim

x → 9

[3f(x) + f(x)g(x)] = 10.

Find

f(9)

Verified Answer :

\(\bf \lim\limits_{x\to 9}\ 3f(x)+f(x)g(x)\quad =\quad 10 \\ \quad \\\\ \lim\limits_{x\to 9}\ 3f(9)+f(9)\underline{g(9)}=10\qquad \qquad \underline{g(9)}=2\qquad thus \\ \quad \\\\ 3f(9)+f(9)+f(9)2=10\implies 3f(9)+2f(9)=10\)

solve for f(9)

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