Find all values of constant a that make the following function continuous on its domain.

Question

Given function: f(x) = {(a sin a x)/ x, x>0}

{2a²+3a-4, x≤0}

Answer 1

lim x→0⁺asinax/x = lim x→0⁺a²(sinax/ax) = a²·1 = a²; a² = 2a² + 3a - 4; a² + 3a - 4 = 0; (a + 4)(a - 1) = 0;

a = 1 or a = - 4