Interval bisection and linear interpolation Quiz

1. For $f(x)=x^2-3$ the root $\sqrt3$ lies in $[1,2]$. After one bisection, which interval contains it?

• A. $[1,1.5]$
• B. $[1.5,2]$
• C. $[1.25,1.75]$
• D. $[1,2]$

2. For $f(x)=x^2-5$ on $[2,3]$, linear interpolation gives which estimate of $\sqrt5$?

• A. $2.25$
• B. $2.5$
• C. $2.4$
• D. $2.2$

3. Which function changes sign on $[1,2]$ yet has no root there (radians)?

• A. $\tan x$
• B. $x^2-2$
• C. $x-1.5$
• D. $x^3-3$

4. A root lies in an interval of width $1$. What is the least number of bisections that guarantees an interval of width at most $0.1$?

• A. $3$
• B. $5$
• C. $10$
• D. $4$

5. $f(1)=-2$ and $f(3)=6$. Linear interpolation gives which estimate of the root?

• A. $2$
• B. $1.5$
• C. $1.75$
• D. $2.5$