# How would you use the Maclaurin series for #e^-x# to calculate #e^0.1#?

We are aware of that

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

To calculate ( e^{0.1} ) using the Maclaurin series for ( e^{-x} ), we can utilize the series expansion of ( e^{-x} ), which is given by:

[ e^{-x} = \sum_{n=0}^{\infty} \frac{(-1)^n}{n!} x^n ]

To find ( e^{0.1} ), substitute ( x = -0.1 ) into the series expansion of ( e^{-x} ) and compute the sum of the series up to a certain number of terms, ensuring an acceptable level of accuracy based on the desired precision.

[ e^{-0.1} = \sum_{n=0}^{\infty} \frac{(-1)^n}{n!} (-0.1)^n ]

Calculate each term of the series for ( n = 0, 1, 2, \ldots ), and sum them to find an approximation for ( e^{-0.1} ). Then, take the reciprocal of this value to find ( e^{0.1} ).

Since ( e^x ) is the reciprocal of ( e^{-x} ), we'll compute ( e^{0.1} ) as:

[ e^{0.1} = \frac{1}{e^{-0.1}} ]

This will give us the desired result.

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 of #f(x)=e^(-2x)# ?
- How do you find the Taylor polynomial of degree 4 for #f(x) = cosh(x)# about #x = 0 # by using the given Taylor polynomial for #e^x#?
- How can you find approximations to the zeros of a function?
- How do you find the maclaurin series expansion of #f(x) = ln abs(1+x^5)#?
- How can you find the taylor expansion of #ln(1-x)# about x=0?

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