deiteresfp

2021-12-28

Evaluate:

My Attempt:

This limit takes

nghodlokl

Beginner2021-12-29Added 33 answers

Without lHospital:

vicki331g8

Beginner2021-12-30Added 37 answers

Since your limit is in the form $\frac{00}{}$ , you can use LHopitals rule.

$\underset{\theta \to \frac{\pi}{4}}{lim}\frac{\mathrm{cos}\theta -\mathrm{sin}\theta}{\theta -\frac{\pi}{4}}=\underset{\theta \to \frac{\pi}{4}}{lim}\frac{\frac{d}{d\theta}(\mathrm{cos}\theta -\mathrm{sin}\theta )}{\frac{d}{d\theta}(\theta -\frac{\pi}{4})}=\underset{\theta \to \frac{\pi}{4}}{lim}(-\mathrm{sin}\theta -\mathrm{cos}\theta )=\dots$

Now that your limit is not indeterminate, you can evaluate your limit by substitution.

Now that your limit is not indeterminate, you can evaluate your limit by substitution.

nick1337

Expert2022-01-08Added 573 answers

If you know that for small x you have

Then your limit is