# How do I rationalize this?

**Calculus**Level 2

Evaluate \( \displaystyle \lim_{x \rightarrow 0} \dfrac{\sin x - \cos x + 1}{\sin x + \cos x -1} \).

**If the answer cannot be inputted into the solution box, select the correct option below and input the number of the option that best fits the correct answer:**

Limit DNE, by approaching \( + \infty\) on both sides of zero: Input 1234

Limit DNE, by approaching \( - \infty \) on both sides of zero: Input 4321

Limit DNE, by not approaching the same value from left and from right of zero, but not approaching \(\pm \infty\) on either side: Input 1324

Limit DNE, by approaching \( -\infty \) from the left of zero, and \(+ \infty\) from the right of zero: Input 1243

Limit DNE, by approaching \( +\infty \) from the left of zero, and \( - \infty \) from the right of zero: Input 3241

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