anonymous
  • anonymous
21.) For what values of x may (x+1)^(1/3) be replaced by x^(1/3), if the allowable error is 0.01? ans... x>192 22.) For what values of x may (x+1)^(1/4) be replaced by x^(1/4), if the allowable error is 0.01? ans... x>73
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.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Can anyone please help with the solution??? Thanks.
mathmate
  • mathmate
21. Solve \[(x+1)^{1/3}-x^{1/3}=0.01\] Depending what maths you're doing, you can solve the equation by trial and error or by Newton's method. You'll find that for x\( \le \)192, the left-hand-side is greater than 0.01. So the answer is x>192. For #22, the process is the same.
anonymous
  • anonymous
Thanks, but what's the solution using approximating formulas (Differentials)?

Looking for something else?

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

More answers

mathmate
  • mathmate
Thanks for providing the context. Let f(x)=x^(1/3) f'(x)=(1/3)x^(-2/3) Using linearization, \( \Delta f = f'(x) \Delta x\) Put \( \Delta x=1\, \ and\ \Delta f = 0.01, \) we get \(f'(x)=\frac{1}{3}x^{-\frac{2}{3}}=0.01/1=0.01 \) solving, \(x=(3*0.01)^{-\frac{3}{2}}=192.45009\ (approx.)\)
anonymous
  • anonymous
Thanks a lot! We haven't discussed linearization yet though (I don't even know what it is yet) but I'll try to understand. Thanks!

Looking for something else?

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