Give the first three non-zero terms of the taylor series for f(x) = tan(x) about x 0· use this to approximate tan(1) and give an upper bound on the error in this approximation

Approximate error = 0.4426

Step-by-step explanation:

f(x)=tanx, a=0

Maclaurin series formula used is given below

f(x)=tanx

f(0)=tan0=0

Hence, the Taylor series for f(x)=tanx is given by

Maclaurin series upper bound error formula used is given as

R_n(x)=|f(x)-T_n(x)|

R_3(x)=|tanx-T_3(x)|

Plugging this value x=1

R_3(x)=|1.5574-1-0.333-0.666|

R_3(x)=|-0.4426|=0.4426

Hence, upper bound on the error approximation

tan(1)=0.4426