Given thatlimx+f(x) = 3, limx+g(x) = 5, limx+h(x) = 0find the limits that exist. If the

Chapter 1, Problem 5

(choose chapter or problem)

Given that

\(\lim _{x \rightarrow+\infty} f(x)=3, \quad \lim _{x \rightarrow+\infty} g(x)=-5, \quad \lim _{x \rightarrow+\infty} h(x)=0\)

find the limits that exist. If the limit does not exist, explain why.

(a)\(\lim _{x \rightarrow+\infty}[f(x)+3 g(x)]\)

(b)\(\lim _{x \rightarrow+\infty}[h(x)-4 g(x)+1]\)

(c)\(\lim _{x \rightarrow+\infty}[h(x)-4 g(x)+1]\)

(d)\(\lim _{x \rightarrow+\infty}[g(x)]^{2}\)

(e)\(\lim _{x \rightarrow+\infty} \sqrt[3]{5+f(x)}\)

(f)\(\lim _{x \rightarrow+\infty} \frac{3}{g(x)}\)

(g)\(\lim _{x \rightarrow+\infty} \frac{3 h(x)+4}{x^{2}}\)

(h)\(\lim _{x \rightarrow+\infty} \frac{6 f(x)}{5 f(x)+3 g(x)}\)

Equation Transcription:

Text Transcription:

Lim_x right arrow +infinity f(x)=3

Lim_x right arrow +infinity g(x)=-5

Lim_x right arrow +infinity h(x)=0

Lim_x right arrow +infinity [f(x)+3g(x)]

Lim_x right arrow +infinity [h(x)-4g(x)+1]

Lim_x right arrow +infinity [f(x)g(x)]

Lim_x right arrow +infinity [g(x)]^2

Lim_x right arrow +infinity cube root of 5+f(x)

Lim_x right arrow +infinity 3/g(x)

Lim_x right arrow +infinity 3h(x)+4/x^2

Lim_x right arrow +infinity 6f(x)/5f(x)+3g(x)