Engineering Board Exam Reviewer · Numerical Methods · hard

Use the secant method on f(x)=x2-2 with x0=1 and x1=2. Find the third approximation x3.

  1. 1.3333
  2. 1.4142
  3. 1.5
  4. 1.4

Answer

D. 1.4

Solution

x2=x1-f(x1)(x1-x0)/f(x1)-f(x0)=2-2(1)/2-(-1)= 43 1.3333. Then f(x2)=- 29 and x3=x2-f(x2)(x2-x1)/f(x2)-f(x1)= 43-(-2/9)(-2/3)/-2/9-2= 43+1/15=1.4.

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