Question: use the definition of continuity and the properties of limits to:

a ) show that the function \(f\left( x \right)={{x}^{2}}+\sqrt{5-x}\) is continuous at x=1

b) find the lim as x approaches 4 g(x), if g(x) is continuous at x=4, and g(4) = 5

c) show that the function \(h\left( x \right)=\frac{x+3}{x-1}\) is continuous on the interval (1, infinity)