Calculus/continuity

Advertisement

Expert: - 3/28/2008


Question
my question is "for what values of x is the function
f(x)= e^sinx / (4 - (x^2 - 9)^1/2)? i'm very glad if you can help me for this question...

Answer
Do you mean for what values of x is f(x) defined or what is it's range?

First, lets take care of the domain.

To answer that question, look at each of the functions in turn.
The basic function is e^x, which is always positive.  Since it's to the sin, note that -1<=sin(x)<=1, so our function is between e^-1 and e^1, or 1/e and e.  That takes care of the top of the function, and now for the bottom.

The function is 4 - (x^2-9)^0.5.  Note that this function is defined in real numbers where (x^2-9) > 0.  Since this is a fraction and this is the denominator, the entire function is undefined when
4^2 = x^2 - 9, which will generate a plus value and a minus value.

Now for the range:  The answer is found in the paragraph before last where I stated that it was between 1/e and e since sin is always between -1 and 1.

Hope this is useful and have a great day. :) - I'm smiling!

Calculus

All Answers

Answers by Expert:

Ask Experts

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.

Experience

Experience in the area: I have tutored students in all areas of mathematics for over 25 years. 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 7,500 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 junior level courses my sophomore year.

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.

©2012 About.com, a part of The New York Times Company. All rights reserved.