Question

Determine c so that f(x) is continuous on the entire real line if f(x)= x^2 when x<=3 and c/x when x>3 ...?

Answer 1

f(x) = x^2 .... if x ≤ 3

f(x) = c /x ... if x > 3

Contidition of continuity => Lim f(x) when x approaches 3 from the right side equals f(3).

f(3) = x^2 = 9

Lim c/ x when x -> 3+ = c/3

Then c / 3 = 9 => c = 3*9 = 27

Answer: c = 27.