# calculus

posted by .

Use the linear approximation
(1+x)^k=1+kx to find an approximation for the function f(x)=1/square root of (4+x) for values of x near zero.

• calculus -

Let's go astep further and also work out the quadratic term using the general formula:

(1+x)^k=1+kx + k(k-1)/2 x^2 +
k(k-1)(k-2)/3! x^3 + ....

f(x)= (4 + x)^(-1/2) =

4^(-1/2) (1 + x/4)^(-1/2) =

1/2 [1 - x/8 + 3/128 x^2 + ...] =

1/2 - x/16 + 3/256 x^2 + ...

## Similar Questions

1. ### calculus

Use the linearization approximation (1+x)^k=1+kx to find an approximation for the function f(x)=(1/square root of 4+x) for values of x near zero.
2. ### calculus

Use the linearization approximation (1+x)^k=1+kx to find an approximation for the function f(x)=(1/square root of 4+x) for values of x near zero.
3. ### Calculus

Estimate delta f using the Linear Approximation and use a calculator to compute the error. f(x)=sqrt(3+x). a=6. delta x=0.1. delta f= With these calculations, we have determined that the square root of ___________ is approximately …
4. ### calculus

Determine an appropriate linear approximation of the function f(x)= the square root of x and use it to approximate the square root of 24.2. Write your answer in decimal form
5. ### Calculus

Use the linear approximation (1+x)^k\approx 1+kx to find an approximation for the function f(x) for values of x near zero. I need help for (3+3x)^(1/3). Please help me!
6. ### Math

Use the linear approximation (1+x)^k=1+kx to find an approximation for the function (3+3x)^(1/3) for values of x near zero. Help would be greatly appreciated!