# Thread: Use differentials (or equivalently, a linear approximation) to approximate...

1. ## Use differentials (or equivalently, a linear approximation) to approximate...

Use differentials (or equivalently, a linear approximation) to approximate as follows: Let and find the equation of the tangent line to at a "nice" point near . Then use this to approximate .

Approximation =

2. The linearization (linear approximation) of f(x) about x = a is given by $\displaystyle f(a) + f'(a)(x-a)$. Let $\displaystyle a = \pi/3$ be the "nice" point and $\displaystyle x = 55\pi/180$ (I'm using radians to make things easier).

3. Originally Posted by nehme007
The linearization (linear approximation) of f(x) about x = a is given by $\displaystyle f(a) + f'(a)(x-a)$. Let $\displaystyle a = \pi/3$ be the "nice" point and $\displaystyle x = 55\pi/180$ (I'm using radians to make things easier).
thanks but do you mind showing maybe the next couple of steps because I have no clue what to do with the given information

4. $\displaystyle f(x) = sin(x)$ implies that $\displaystyle f'(x) = cos(x)$. Plug the values of x and a that I suggested into $\displaystyle f(a) + f'(a)(x-a)$.