# How do you find the first two nonzero terms in Maclaurin's Formula and use it to approximate #f(1/3)# given #f(x)=tanx#?

So that:

Now consider:

so:

The term:

By signing up, you agree to our Terms of Service and Privacy Policy

Maclaurin's Formula is a special case of Taylor's Formula centered at ( x = 0 ). The formula states:

[ f(x) = f(0) + f'(0)x + \frac{f''(0)}{2!}x^2 + \frac{f'''(0)}{3!}x^3 + \cdots ]

For the function ( f(x) = \tan(x) ), the first two nonzero terms in Maclaurin's Formula are:

[ f(0) = \tan(0) = 0 ] [ f'(0) = \sec^2(0) = 1 ]

Thus, the approximation becomes:

[ f(x) ≈ 0 + 1x = x ]

To approximate ( f(1/3) ), substitute ( x = \frac{1}{3} ) into the approximation:

[ f\left(\frac{1}{3}\right) ≈ \frac{1}{3} ]

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the maclaurin series expansion of #f(x) = x/(1-x)#?
- How do you use Taylor series for #sin(x)# at #a = pi/3#?
- How do you find the taylor series for #f(x)=xcos(x^2)#?
- How do you find the power series representation for the function #f(x)=sin(x^2)# ?
- How do you find the power series representation for the function #f(x)=(1+x)/(1-x)# ?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7