Answer:
According what I can read, I have the following statements:
[tex]\lim_{x \to 2} f(x) = 1[/tex]
[tex]\lim_{x \to 2} g(x) = -4[/tex]
[tex]\lim_{x \to 2} h(x) = 0[/tex]
a) Applying properties of limits
[tex]\lim_{x \to 2} f(x) + 5g(x) = \lim_{x \to 2} f(x) + 5 \lim_{x \to 2} g(x) = 1 + 5*-4 = -19[/tex]
b) Applying properties of limits
[tex]\lim_{x \to 2} g(x)^{3} = {(\lim_{x \to 2} g(x))}^{3} = (-4)^{3} = -64[/tex]
c) Applying properties of limits
[tex]\lim_{x \to 2} \sqrt{f(x)} = \sqrt{\lim_{x \to 2} f(x)} = \sqrt{1} = 1[/tex]
d) Applying properties of limits
[tex]\lim_{x \to 2} 4*g(x)*f(x) = 4*\lim_{x \to 2} g(x)*\lim_{x \to 2} f(x) = 4*-4*1 =-16[/tex]
e) Applying properties of limits
[tex]\lim_{x \to 2} g(x)*h(x) = \lim_{x \to 2} g(x)*\lim_{x \to 2} h(x) = -4*0 =0[/tex]
f) Applying properties of limits
[tex]\lim_{x \to 2} g(x)*h(x)*f(x) = \lim_{x \to 2} g(x)*\lim_{x \to 2} h(x)*\lim_{x \to 2} f(x = -4*0*1 =0[/tex]
