Problem 1
In Problems 1-24, evaluate each improper integral or show that it diverges. \(\int_{100}^{\infty} e^{x} d x\)
Problem 1
In Problems \(1-32\), evaluate each improper integral or show that it diverges. $$ \text { 1. } \int_{1}^{3} \frac{d x}{(x-1)^{1 / 3}} $$
Problem 1
Find each limit. Be sure you have an indeterminate form before applying l'Hôpital's Rule. $$ \lim _{x \rightarrow \infty} \frac{\ln x^{10000}}{x} $$
Problem 1
Find the indicated limit. Make sure that you have an indeterminate form before you apply l'Hôpital's Rule. $$ \lim _{x \rightarrow 0} \frac{2 x-\sin x}{x} $$
Problem 2
Find each limit. Be sure you have an indeterminate form before applying l'Hôpital's Rule. $$ \lim _{x \rightarrow \infty} \frac{(\ln x)^{2}}{2^{x}} $$
Problem 2
Find the indicated limit. Make sure that you have an indeterminate form before you apply l'Hôpital's Rule. $$ \lim _{x \rightarrow \pi / 2} \frac{\cos x}{\frac{1}{2} \pi-x} $$
Problem 2
Evaluate each improper integral or show that it diverges. \(\int_{-\infty}^{-5} \frac{d x}{x^{4}}\)
Problem 3
Find each limit. Be sure you have an indeterminate form before applying l'Hôpital's Rule. $$ \lim _{x \rightarrow \infty} \frac{x^{10000}}{e^{x}} $$
Problem 3
Find the indicated limit. Make sure that you have an indeterminate form before you apply l'Hôpital's Rule. $$ \lim _{x \rightarrow 0} \frac{x-\sin 2 x}{\tan x} $$
Problem 3
Evaluate each improper integral or show that it diverges. \(\int_{1}^{\infty} 2 x e^{-x^{2}} d x\)
