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 \(\underset{x\to 4}{\mathop{\lim }}\,g\left( x \right)\), 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)

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