Posted by **kendra** on Wednesday, April 18, 2012 at 11:33am.

use differentials to approximate the value of the squareroot of 4.3

- calculus -
**MathMate**, Wednesday, April 18, 2012 at 5:21pm
Let

f(x)=sqrt(x)=x^(1/2)

f'(x)=1/(2sqrt(x))

and

f(x0+Δx)=f(x0)+f'(x0)*Δx (approx.)

or

Δx=(f(x0+Δx)-f(x0))/f'(x0) approx.

Knowing that 2^2=4, and 2.1^2=4.41

Try x0=2

Δx=(4.3-2^2)/(1/(2*2)

=0.3/(4)

=0.075

or

Approximately, x+Δx=2+.075=2.075

(check: 2.075^2=4.305625)

Try x0=2.1, x0^2=4.41...

to get a still better approximation.

## Answer this Question

## Related Questions

- calculus - use differentials to approximate the value of the expression: square ...
- calculus - Use differentials (or equivalently, a linear approximation) to ...
- Algebra - I need some help figuring these. Compute each product and simplify ...
- Algebra - I need some help figuring these. Compute each product and simplify the...
- calculus! - Use differentials to approximate the maximum error propagated when ...
- Applied Calculus - Use differentials to approximate the quantity (give answer to...
- calculus - write the expression in the form bi, where b is the real number ...
- algebra - ^5 squareroot of x^20 *my answer x^4 ^3 squareroot of 729/343 my ...
- Calculus-Solved-Why is this wrong? - use differentials to approximate the change...
- Calculus-Differentials-Check please? - if the sides of a cube are measured with ...

More Related Questions