Question

question 1: determine which of the following conjuctions of funtions are liner independent

x + s.pupr.edu/webapps/assessment/take/launch.jsp?course_assessment_id-_56871_1&course_id=_25241_1&c Question Completion Status: QUESTION 1 Determine cuál de los siguientes conjuntos de funciones es linealmente independiente. -1x2x 3x, x cosºx, sinºx, 1 ex, Inx, x+xinx Ninguna de las anteriores QUESTION 2 Encuentre el Wronskian para f(x) = cos(Inx), S(x)=sin (In x) cos" (In x)-sin (Inx) cos' (In x) -sin (In x) Click Sque and Submit to manu a l

question 2: find the Wroskian for... last options is E.) none of the above

Answer 1

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For wronskian W=1/x is answer ....

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43@ 1 1 ,x, 2x ? are not linearly independent because ax can be written as aux (mans come veetector can be written as Linear Combination of other vector) 6 f3, x, sc2y < P (R) - this is Basis of PLUR) t th { 3, 2, 22y are hirearly independet 0 cose, sink, l it is also not Because Linearly independent hirear 000 - one can be written as Combination of other. ) Sin ex) + cos(x) = 1 mylin

sol! h find wronskien. - fax, fr= lnx Wolfio fulf) = l fi fr f3= x + x lnx fo = I x xtalnx lnx xtalux , 1 1 2x enx te! enx t2 = x + fol entry - n* [ 1 ] + +62+2 (-43) = ☆ f inets ente tem = $+bola +2 - ent - enx-5 « 12- en (ms) # " So hirearty 1. independent.

John's Given f(x) = cos (ene) , focx) = sin(ln(a)) . Wl fix fa) = l file) fins , ' fiius 'X) / ** f(x) = cos (enin) f'(x) = -sintlnr). Ź f fx (x) = sin(en(x)) tz'in) = cos (ln(e) = Sin (en (n)) , Jo Wlf. f) = . l cos (lnx) . 1-sin (en (4) / cas (encx): 1 Cos" (ln(n)) - $ + sinºlence). f Ccos?cence) + sin? (entus) = Sin xet cos+z=2 so Wlfiefel = & Answers