Use Algebraic Methods to determine the limit. $$ \lim _{\theta \rightarrow \pi / 4} \frac{\sin ^{2} \theta-\cos ^{2} \theta}{\sin \theta-\cos \theta} $$

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1. Recognize that the numerator is a difference of squares:
   $$
   \sin^2 \theta - \cos^2 \theta = (\sin \theta - \cos \theta)(\sin \theta + \cos \theta)
   $$

2. Substitute this factorization into the limit:
   $$
   \lim_{\theta \rightarrow \pi/4} \frac{(\sin \theta - \cos \theta)(\sin \theta + \cos \theta)}{\sin \theta - \cos \theta}
   $$

3. Cancel the common factor $$\sin \theta - \cos \theta$$ (noting that this cancellation is valid since the argument of the limit approaches, but is not equal to, a point where the factor is zero):
   $$
   \lim_{\theta \rightarrow \pi/4} (\sin \theta + \cos \theta)
   $$

4. Evaluate the limit by substituting $$\theta = \pi/4$$:
   $$
   \sin \frac{\pi}{4} + \cos \frac{\pi}{4} = \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2} = \sqrt{2}
   $$

5. Thus, the limit is:
   $$
   \sqrt{2}
   $$
The limit is $$\sqrt{2}$$.

Use Algebraic Methods to determine the limit.

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