Question

Determine whether the functions y, and y, are linearly dependent on the interval (0,1). yn = sec ?t-tant, y = 3 Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Since y Dy on (0,1), the functions are linearly independent on (0,1). (Simplify your answer.) OB. Since y, yon (0,1), the functions are linearly dependent on (0.1). (Simplify your answer.) O C. Since y, is not a constant multiple of y2 on (0,1), the functions are linearly independent on (0,1). OD. Since y, is not a constant multiple of yz on (0,1), the functions are linearly dependent on (0,1).

Answer 1

y, = sectatan't ,1223 consider , h() = 19, 7 . sect-tastt : 1 yil Ya!? 2sect sectitant el '-lant seit 01. Wct) = 0 -3 (25eet teint ~2 tant seet) ( Note Wict), -360). . Ict) =0 that & sect = sect, tant of faint - selt . d sect = 2 sectos sect) ---by chain rule t tari't = 2tant Content) --- by Chain rule i WCH)=0., for any t € (0,1). ii yo fya are linearly dependent. We know that it taño = seco = I=se&o-tanto ... here is seet-tan't 3- 3 (sert-tant) - Yo = 3.91 Answer option-BS