You are here:

# Calculus/limits at infinity

Question
I don't understand why the limit of the function xsin(x)=infinity as x approaches infinity !?
I would really appreciate your help :)

The limit is really undefined.

Lets start by saying that f(x) = x*sin(x).

The limit(x->infinity)[f(x)] is undefined.
Given any y0 value, no matter what x0 is chosen,
an x value can be found such that f(x0) = y0.

This is because sin(x) always varies between -1 and 1.
This means the limit always varies between -x and x.
As x goes to infinity, the function then varies between -infinity and infinity.'

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 9 Politeness = 10 Comment Thank You :)

Calculus

Volunteer

#### Scotto

##### Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology (reproduction, insusion of chemicals into bloodstream).

##### Experience

Experience in the area: I have tutored students in all areas of mathematics since 1980. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 8,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few courses at college a year early.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.