Posted by **kale** on Friday, August 31, 2012 at 11:42am.

limit as delta x approaches 0 when f(x) = 4/ sqr x

Have to use the (F(x+delta x)-f(x))/delta x method

- calculus -
**Steve**, Friday, August 31, 2012 at 2:10pm
just plug and chug

[f(x+h)-f(x)]/h

4(x+h)^(-1/2) - 4*x^(-1/2)

Now, to evaluate (x+h)^(-1/2), use the binomial theorem:

(a+b)^n = a^n + n*a^(n-1)*b^1 + n(n-1)/2 * a^(n-1)b^2 + ...

(x+h)^(-1/2) = x^(-1/2) + (-1/2)*x^(-3/2)*h + (-1/2)(-3/2)/2 * x^(-5/2)h^2 + ...

(x+h)^(-1/2) - x^(-1/2) = (-1/2)*x^(-3/2)*h + (-1/2)(-3/2)/2 * x^(-5/2)h^2 + ...

divide all that by h to get

(-1/2)*X^(-3/2) + (-1/2)(-3/2)/2 * x^(-5/2)h + ...

= -1/2x^(-3/2) + 3/8x^(-5/2)*h + ...

As h->0, all the terms with h disappear, leaving just

-1/2 x^(-3/2)

multiply that by 4 from the original function, and you get

-2x^-3/2 = -2/√x^{3}

## Answer This Question

## Related Questions

- CALCULUS help please - Find the following limit where f(x) = 4x^2 − 3x. ...
- Calculus-Solved - Incorrect - calculate delta y for f(x)= x^(3/2) with x= 4 and ...
- CHEMISTRY - Please explain. The enthalpy changes for two different hydrogenation...
- Chemistry - Please explain. The enthalpy changes for two different ...
- Chemistry(Please check answers) - 1) For a reaction delta Go is more negative ...
- calculus - Find the following limit where f(x) = 4x2 − 3x. limit delta x...
- Calculus - I know the derivative of x is 1, but I'm having a hard time proving ...
- equibrium - help! - Consider the reaction CO(g) + H2O(g) <--> CO2(g) + H2(...
- math - Compute delta(y) and dy for the given values of x and dx=delta(x) y=x^2...
- Chemistry(DrBob222) - So, i did this lab, a solubility and thermodynamics lab of...

More Related Questions