Verified answer

a)

lim [f(x) + 4g(x)] = lim x-->2 f(x) + 4 lim x-->2 g(x) = 2(4)+ 4(-2) = 0

x→2

b)

(b)

lim [g(x)]^3 = lim x-->2 g(x) lim x-->2 g(x) lim x-->2 g(x) = (-2)^3 = -8

x-->2

(c)

lim sqrt[f(x)] = sqrt(lim x-->2 f(x)) = sqrt(4) = 2

x→2

(d)

lim 5f(x)/g(x)

x→2

= 5 lim x-->2 f(x) / lim x--> 2 g(x) = 5(4)/(-2) = -10

(e)

lim g(x)/h(x) = lim x-->2 g(x) / lim h-->2 h(x) = -2/0 = (does not exist)

lim x→2

(f)

lim (g(x)h(x))/f(x)

x→2

= lim x-->2 g(x) lim x-->2 h(x) / lim x-->2 f(x) = (-2)(0) / 4 = 0