1 (b) [1.0pt]: Show that the function 1+ g(x) can be expanded to the third order...

 

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1 (b) [1.0pt]: Show that the function 1+ g(x) can be expanded to the third order in powers of (1-1) as: where 1 1+ g(x) 1-Ax+ Bx - Cx dg dg A - B -[(4)-1] = . dx 2 dx dg C c = [ (ds) - - dx HINT: use the chain rule. dg dg dx dx + 1 dg 6 dx with g(0) = 0, (c) [1.0pt]: Using the result form (b), show that 1 Ho(1 16) + ( 1 + 2 ) HZ(1 160) ( 1 + 9 + 0 ) HZ(1 1 a(t) 1 (b) [1.0pt]: Show that the function 1+ g(x) can be expanded to the third order in powers of (1-1) as: where 1 1+ g(x) 1-Ax+ Bx - Cx dg dg A - B -[(4)-1] = . dx 2 dx dg C c = [ (ds) - - dx HINT: use the chain rule. dg dg dx dx + 1 dg 6 dx with g(0) = 0, (c) [1.0pt]: Using the result form (b), show that 1 Ho(1 16) + ( 1 + 2 ) HZ(1 160) ( 1 + 9 + 0 ) HZ(1 1 a(t)