Wednesday

October 22, 2014

October 22, 2014

Posted by **DJ** on Tuesday, October 4, 2011 at 10:06am.

hint: 0< |sqrt(x)-sqrt(c)|= (|x-c|)/(sqrt(x)+sqrt(c))<(1/(sqrt(c))*|x-c|

- Calculus -
**Count Iblis**, Tuesday, October 4, 2011 at 2:29pmlim x->c (sqrt(x)) = (sqrt(c))

means that the closer x is chosen to c the closer sqrt(x) comes to sqrt(c). To prove that, you need to show that making |sqrt(x) - sqrt(c)| smaller than some arbitrary epsilon is always possible by restricting x to some interval around c. Since epsilon can be any number larger than zero, this means that this interval around zero exists no matter how small epsilon is chosen. So, even if epsilon = 0.000000000001, there is stll a small interval around c for which the square root function is within 0.000000000001 of c.

From the inequalities:

0< |sqrt(x)-sqrt(c)|= (|x-c|)/(sqrt(x)+sqrt(c))<(1/(sqrt(c))*|x-c|

you can see that to require

|sqrt(x)-sqrt(c)| < epsilon

it is enough to require that:

|x-c| < sqrt(c) epsilon

So, we see that for arbitrary

epsilon > 0 there indeed does exist a delta > 0 such that for |x-c| < delta we have that

|sqrt(x) - sqrt(c)| < epsilon

**Answer this Question**

**Related Questions**

Math Help please!! - Could someone show me how to solve these problems step by ...

math calculus please help! - l = lim as x approaches 0 of x/(the square root of...

Mathematics - sqrt 6 * sqrt 8 also sqrt 7 * sqrt 5 6.92820323 and 5.916079783 So...

Math(Roots) - sqrt(24) *I don't really get this stuff.Can somebody please help ...

math,algebra,help - Directions are simplify by combining like terms. x radiacal ...

Math - How do you find a square root of a number that's not a perfect square? I'...

Inequality - When I solve the inquality 2x^2 - 6 < 0, I get x < + or - ...

Calculus - Please look at my work below: Solve the initial-value problem. y'' + ...

Math/Calculus - Solve the initial-value problem. Am I using the wrong value for ...

Calculus - show lim x->3 (sqrt(x)) = (sqrt(c)) hint: 0< |sqrt(x)-sqrt(c...