Question

Suppose f and g are continuous functions such that
g(5) = 3 and lim x → 5 [3f(x) + f(x)g(x)] = 18. Find f(5).

Answer 1

Hint:
You can break up the limit to go from
\[\Large \lim_{x\to 5}(3f(x)+f(x)g(x)) = 18\]
to
\[\Large 3\lim_{x\to 5}(f(x))+\lim_{x\to 5}(f(x))*\lim_{x\to 5}(g(x)) = 18\]

Answer 2

lim x → 5 [3f(x) + f(x)g(x)] = 18

hint when a function is continues then \( \lim _{x→x_0}=f(x_0)\)
also u can use properties of limits
1_ \( \lim f\pm g =\lim f \pm \lim g\)

2_ \( \lim k f =k\lim f \) s.t k is real number