Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 21/Solution 1

Recall that the Taylor series for a function ${\textstyle y(t)}$ is

$$y(t)=y(t_{0})+y'(t_{0})(t-t_{0})+....$$

We are given ${\textstyle t_{0}=0}$, ${\textstyle t-t_{0}=1/10=\Delta t}$, and we have an equation for ${\textstyle y'(t)}$. Substituting this all in gives

$${\begin{aligned}y&=y(0)+y'(0)(\Delta t)\\&=-1+(-(-1)(-1-2)(-1-11))({\frac {1}{10}})\\&=-1+3.3\\&=2.3.\end{aligned}}$$

The solution is approximately ${\textstyle y=2.3}$.