# Thread: calculus three. 2nd degree taylor polynomial

1. ## 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

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 $\displaystyle (a,b,c)$

$\displaystyle f(a,b,c) + f_x(a,b,c)(x-a) + f_y(a,b,c)(y-b) + f_z(a,b,c)(z-c)$

$\displaystyle + f_{xx}(a,b,c)\frac{(x-a)^2}{2!} + f_{xy}(a,b,c)(x-a)(y-b) + f_{xz}(a,b,c)(x-a)(z-c)$

$\displaystyle + f_{yy}(a,b,c)\frac{(y-b)^2}{2!} + f_{yz}(a,b,c)(y-b)(z-c) + f_{zz}(a,b,c)\frac{(z-c)^2}{2!}$

3. 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!