Question

Question 32 Suppose f(x) ={ mx^2 + n, x < 0
nx + m, 0 ≤ x ≤ 1 For what integers m and n does lim(x-->0) f(x) and lim(x-->1) f(x) exist?
nx^3 + m, x > 1 }

Class XI - Limits and Derivatives Page 303

Answer 1

concept: limit exist at x = 0 and 1.
it means
     limit(x→0⁻)f(x) =limit(x→0⁺)f(x)
similarly,
  limit(x→1⁻)f(x) =limit(x→1⁺)f(x)

 limit(x→0⁻)f(x) =m(0)^2+n = n
 limit(x→0⁺)f(x) = n(0)+m = m
         n = m
hence, all integers values of m and n   are possible  where  m = n

 limit(x→1⁻)f(x) = n + m
 limit(x→1⁺)f(x) = n +m
hence all integers values of m and n  are possible for lim(x→1)