Engineering Board Exam Reviewer · Numerical Methods · medium
Use the bisection method on f(x)=x3-x-1 with the starting interval [1,2]. What is the third midpoint computed?
- 1.25
- 1.5
- 1.3125
- 1.375
Answer
D. 1.375
Solution
Midpoint 1: 1.5, f(1.5)=0.875>0, so the root is in [1,1.5]. Midpoint 2: 1.25, f(1.25)=-0.297<0, so the root is in [1.25,1.5]. Midpoint 3: 1.25+1.5/2=1.375.
More Numerical Methods questions
- Apply one Newton-Raphson iteration to f(x)=x3-2x-5 starting from x0=2.
- Apply one Newton-Raphson iteration to f(x)=x2-5 starting from x0=2.
- Use the trapezoidal rule with n=2 subintervals to approximate 02x2,dx.
- Use the secant method on f(x)=x2-2 with x0=1 and x1=2. Find the third approximation x3.
- Use one step of the fourth-order Runge-Kutta method with h=0.2 to estimate y(0.2) for y'=x+y, y(0)=1.
- Use Simpson's 13 rule with n=4 to approximate 0π x,dx.
- Use Euler's method with h=0.1 to estimate y(0.2) for y'=x+y, y(0)=1.