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Math Help - calculus three. 2nd degree taylor polynomial

  1. #1
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    Unhappy calculus three. 2nd degree taylor polynomial

    find the second degree taylor polynomial for the given function at the point indicated

    f(x,y,z)= x+ye^z
    a= (1,1,0)

    i somewhat remember taylor polynomials from calc two, but can anyone start me off here please? any hints would be super
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  2. #2
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    Quote Originally Posted by andyaddition View Post
    find the second degree taylor polynomial for the given function at the point indicated

    f(x,y,z)= x+ye^z
    a= (1,1,0)

    i somewhat remember taylor polynomials from calc two, but can anyone start me off here please? any hints would be super
    About (a,b,c)

     <br />
f(a,b,c) + f_x(a,b,c)(x-a) + f_y(a,b,c)(y-b) + f_z(a,b,c)(z-c) <br />

     <br />
+ f_{xx}(a,b,c)\frac{(x-a)^2}{2!} + f_{xy}(a,b,c)(x-a)(y-b) + f_{xz}(a,b,c)(x-a)(z-c)

     <br />
+ f_{yy}(a,b,c)\frac{(y-b)^2}{2!} + f_{yz}(a,b,c)(y-b)(z-c) + f_{zz}(a,b,c)\frac{(z-c)^2}{2!}
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  3. #3
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    For this particular function, it is enough to remember that [tex]e^z= \sum_{n=0}^\infty \frac{z^n}{n!}[tex]. Now multiply by y and add x!
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