Posted by **Sarita** on Saturday, April 3, 2010 at 10:26am.

A) How do you prove that if 0(<or=)x(<or=)10, then 0(<or=)sqrt(x+1)(<or=)10?

B) So once that is found, then how can you prove that if 0(<or=)u(<or=)v(<or=)10, then 0(<or=)sqrt(u+1)(<or=)sqrt(v+1)(<or=)10?

- calculus -
**Damon**, Saturday, April 3, 2010 at 3:34pm
How do you prove that if 0(<or=)x(<or=)10, then 0(<or=)sqrt(x+1)(<or=)10?

===========================

does the square root increase (is the derivative positive) as x goes from 0 to 10 ?

If so the left side of the domain is minimum and the right side is maximum of the function and we only need to test the ends.

d (x+1)^.5 / dx = .5 /sqrt(x+1)

that is positive everywhere in the domain so all we have to prove is the end points.

0 </= x </= 10

if x = 0

sqrt x+1 = sqrt 1 = 1

if x = 10

sqrt x+1 = sqrt 11 = 3.32

so

1 </ sqrt(x+1) </= 3.32

## Answer This Question

## Related Questions

- calculus - A) How do you prove that if 0(<or=)x(<or=)10, then 0(<or=)...
- calculus - A) How do you prove that if 0(<or=)x(<or=)10, then 0(<or=)...
- Calculus - A) How do you prove that if 0(<or=)x(<or=)10, then 0(<or=)...
- calculus - A) How do you prove that if 0(<or=)x(<or=)10, then 0(<or=)...
- Math Help please!! - Could someone show me how to solve these problems step by ...
- Calculus - Please look at my work below: Solve the initial-value problem. y'' + ...
- calculus - prove that d/dx 4x .√(x + √x) = 6x+5 (x)1/2/√(x...
- math calculus please help! - l = lim as x approaches 0 of x/(the square root of...
- Real Analysis (Math) - Prove: [1/sqrt(2)] [sqrt(a) + sqrt(b)] <= sqrt(a + b...
- Math/Calculus - Solve the initial-value problem. Am I using the wrong value for ...

More Related Questions