Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
if\[f'(x)=\frac{1}{1+x+x^2+x^3}\],\[g'(x)=\frac{x}{1+x+x^2+x^3}\]and \(f(0)=g(0)\)
Find value of \(f(1)g(1)\)
 one year ago
 one year ago
if\[f'(x)=\frac{1}{1+x+x^2+x^3}\],\[g'(x)=\frac{x}{1+x+x^2+x^3}\]and \(f(0)=g(0)\) Find value of \(f(1)g(1)\)
 one year ago
 one year ago

This Question is Closed

EulerGroupieBest ResponseYou've already chosen the best response.1
The Rational Zero Theorem suggests that (x1) or (x+1) may be factors of the denominators. Using polynomial long division (or synthetic division) indicates that (x+1) is a factor. Use the resulting factored denominator with partial fraction decomposition to break both functions into something that can be integrated. Integrate both functions with separately marked added constants (I used subscript f and g). Set f(x)=g(x) substituting x=0 in for both functions to find what the constants should be. You won't find the exact constants, but you will see how they relate to each other. Now substitute x=1 into f(x)g(x). Would you like the thrill of discovery, or would you like to see my details?
 one year ago

helder_edwinBest ResponseYou've already chosen the best response.1
\[ f(1)g(1)=\arctan 1\]
 one year ago

EulerGroupieBest ResponseYou've already chosen the best response.1
Not exactly what I got... but close
 one year ago

EulerGroupieBest ResponseYou've already chosen the best response.1
hey... I think you are right...arctan x with x=1... yup. I incorrectly put x^2+1 into my argument, but it should be just x...nice!
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.