Limit of cos⁡(kt+kux) as k→0wherek=21−a2u=b(6−k2)and a and b are real numbers?

For small cos⁡(z)≈1−z22. For small k,u≈6b. Thencos⁡(k(x+6bt))≈1−k22(t+6xb)2

Get the answer to "Limit of cos⁡(kt+kux) as k→0wherek=21−a2u=b(6−k2)and a and b..."

Zack Mora

2022-03-24

Limit of

\cos (k t + k u x)

k \to 0

where

k = 2 \sqrt{1 - a^{2}}

u = b (6 - k^{2})

and a and b are real numbers?

Chelsea Chen

Beginner2022-03-25Added 5 answers

For small

\cos (z) \approx 1 - \frac{z^{2}}{2}

. For small

k, u \approx 6 b

. Then

\cos (k (x + 6 b t)) \approx 1 - \frac{k^{2}}{2} {(t + 6 x b)}^{2}

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?