Multi-Variable Taylor Series Expansion, Ignoring some terms possible? Will it still give a good approx.

So I'm computing a second order Taylor series expansion on a function that has multiple variables. So far I have this

I(x,y,t)=dI/dx(change in x)+dI/dy(change in y)+dI/dt(change in t)+2nd order terms

Would it still be a better approximation than just he first order if I included some second order terms and not other or what? Thanks,

Chris

This would depend on the accuracy required, the error in the variables, etc.
I would want to use all second order terms and see the effect of omitting
some of them.