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# Like terms Calculator

## Get detailed solutions to your math problems with our Like terms step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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### Difficult Problems

1

Solved example of Like terms

$\lim_{x\to0}\left(\frac{e^X-1-X}{X^2}\right)$
2

As the limit results in indeterminate form, we can apply L'Hôpital's rule

$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(e^x-1-x\right)}{\frac{d}{dx}\left(x^2\right)}\right)$
3

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(e^x-1-x\right)}{2x}\right)$
4

The derivative of a sum of two functions is the sum of the derivatives of each function

$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(e^x\right)+\frac{d}{dx}\left(-1\right)+\frac{d}{dx}\left(-x\right)}{2x}\right)$
5

The derivative of the constant function is equal to zero

$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(-x\right)+\frac{d}{dx}\left(e^x\right)}{2x}\right)$
6

The derivative of the linear function times a constant, is equal to the constant

$\lim_{x\to0}\left(\frac{-1+\frac{d}{dx}\left(e^x\right)}{2x}\right)$
7

Applying the derivative of the exponential function

$\lim_{x\to0}\left(\frac{-1+e^x}{2x}\right)$
8

As the limit results in indeterminate form, we can apply L'Hôpital's rule

$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(-1+e^x\right)}{\frac{d}{dx}\left(2x\right)}\right)$
9

The derivative of the linear function times a constant, is equal to the constant

$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(-1+e^x\right)}{2}\right)$
10

The derivative of a sum of two functions is the sum of the derivatives of each function

$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(-1\right)+\frac{d}{dx}\left(e^x\right)}{2}\right)$
11

The derivative of the constant function is equal to zero

$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(e^x\right)}{2}\right)$
12

Applying the derivative of the exponential function

$\lim_{x\to0}\left(\frac{e^x}{2}\right)$
13

The limit of the product of a function and a constant is equal to the limit of the function, times the constant: $\displaystyle \lim_{t\to 0}{\left(2t\right)}=2\cdot\lim_{t\to 0}{\left(t\right)}$

$\frac{1}{2}\lim_{x\to0}\left(e^x\right)$
14

Evaluating the limit when $x$ tends to $0$

$\frac{1}{2}e^0$
15

Simplifying

$\frac{1}{2}$

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