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 April 11th, 2015, 07:51 AM #1 Member     Joined: Jul 2012 Posts: 60 Thanks: 0 Math Focus: Calculus Fake multivariable function notation So let's say I had a multivariable function, random example: $\displaystyle f(x,t)=x^2 + x\cdot t + \sin{t}$ But what if x was actually a function of t itself. Would the following notation be permitted? $\displaystyle f(x(t),t)=x^2(t) + x(t)\cdot t + \sin{t}$ And also, does that imply the following? $\displaystyle 1^\circ \; f(x(t-t_0),t)=x^2(t-t_0) + x(t-t_0)\cdot t + \sin{t} \\$ $\displaystyle 2^\circ \; f(x(t),t-t_0)=x^2(t-t_0) + x(t-t_0)\cdot (t-t_0) + \sin{(t-t_0)}$ The first one makes sense, but the second one seems a bit strange. Is there a better way to write this down? Thanks.
 April 11th, 2015, 10:10 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,835 Thanks: 2162 The first interpretation would be correct.

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