Carissa15
  • Carissa15
Apply the mean value Theorem to f(x)=In(1+x) to show that x1+x0. I am still unsure of this, I think I need to substitute any x>0 for each of the 3 equations and their derrivative x1+x 0 each equation will be less than the last?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Carissa15
  • Carissa15
\[f(x)=\ln(+x)\] is the original equation and I have to use the mean value theorem to show that\[\frac{ x }{1+x } < \ln(1+x) < x, \] for x > 0.
IrishBoy123
  • IrishBoy123
I'm on mobile and can't do any latex or drawing So, to solve note simple statement of MVT: f'(c) = [ f(b) - f(a) ] / [b -a] Using a = 0, b = x, calculate f'(c) in terms of x. Then look separately at inequalities (A) c< b, ie c< x and (B) c> a,ie c> 0 Some faffing around and you will get there
Carissa15
  • Carissa15
Thank you so much, all sorted now. Big help. Thanks

Looking for something else?

Not the answer you are looking for? Search for more explanations.