Calculus: Fill in the blanks: If f and g are continuous functions with f(2) = 9 and limx→2[2f(x) + 3g(x)] = 6. Use the properties limits and
continuity to find g(2). Soln: Since we have an equation above,
working first on the left hand side: limx→2[2f(x) + 3g(x)] =
= (*)
Since f and g are both continuous and f(2) = 9. By definition,
limx→2 f(x) = = and limx→2 g(x) = (∗∗)
Now, continuing from line (∗) above together with line (∗∗) , we have
———————————————- = ————————————–= 6
——————— = 6
3g(2) = 6 − =
g(2) =