Question

Given that lim x → 2 f ( x ) = 1 lim x → 2 g ( x ) = − 4 lim x → 2 h ( x ) = 0 limx→2f(x)=1 limx→2g(x)=-4 limx→2h(x)=0, find the limits, if they exist. (If an answer does not exist, enter DNE.) (a) lim x → 2 [ f ( x ) + 5 g ( x ) ] limx→2[f(x)+5g(x)] (b) lim x → 2 [ g ( x ) ] 3 limx→2[g(x)]3 (c) lim x → 2 √ f ( x ) limx→2f(x) (d) lim x → 2 4 f ( x ) g ( x ) limx→24f(x)g(x) (e) lim x → 2 g ( x ) h ( x ) limx→2g(x)h(x) (f) lim x → 2 g ( x ) h ( x ) f ( x ) limx→2g(x)h(x)f(x)

Answer 1

Answer:

According what I can read, I have the following statements:

$\lim_{x \to 2} f(x) = 1$

$\lim_{x \to 2} g(x) = -4$

$\lim_{x \to 2} h(x) = 0$

a) Applying properties of limits

$\lim_{x \to 2} f(x) + 5g(x) = \lim_{x \to 2} f(x) + 5 \lim_{x \to 2} g(x) = 1 + 5*-4 = -19$

b) Applying properties of limits

$\lim_{x \to 2} g(x)^{3} = {(\lim_{x \to 2} g(x))}^{3} = (-4)^{3} = -64$

c) Applying properties of limits

$\lim_{x \to 2} \sqrt{f(x)} = \sqrt{\lim_{x \to 2} f(x)} = \sqrt{1} = 1$

d) Applying properties of limits

$\lim_{x \to 2} 4*g(x)*f(x) = 4*\lim_{x \to 2} g(x)*\lim_{x \to 2} f(x) = 4*-4*1 =-16$

e) Applying properties of limits

$\lim_{x \to 2} g(x)*h(x) = \lim_{x \to 2} g(x)*\lim_{x \to 2} h(x) = -4*0 =0$

f) Applying properties of limits

$\lim_{x \to 2} g(x)*h(x)*f(x) = \lim_{x \to 2} g(x)*\lim_{x \to 2} h(x)*\lim_{x \to 2} f(x = -4*0*1 =0$