Numerical methods worksheet with answers

Free printable Numerical methods worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
xyx₀ = 4

Apply Newton–Raphson to f(x) = ln x + x − 4 with the starting value x₀ = 4. Find x2.

f(x) = ln x + x − 4f′(x) = 1/x + 1x₀ = 4
x2 =
2.Easy
xyx₀ = 1

Apply Newton–Raphson to f(x) = x³ − x − 2 with the starting value x₀ = 1. Find x2.

f(x) = x³ − x − 2f′(x) = 3x² − 1x₀ = 1
x2 =
3.Medium
xy00.16670.33330.50.66670.83331

Approximate ∫01 √(1 + x³) dx with the trapezoid rule using n = 6 strips. Give T.

f(x) = √(1 + x³)[a, b] = [0, 1]n = 6
T =
4.Medium
xy00.33330.666711.3331.6672

Approximate ∫02 √x·e−x dx with Simpson's rule using n = 6 strips. Give S.

f(x) = √x·e−x[a, b] = [0, 2]n = 6
S =
5.Hard
00.20.40.60.8−3−2−1ty(0, −1)

Use Euler's method with h = 0.2 for y′ = 1.5y, y(0) = −1 to estimate y4 ≈ y(0.8).

y′ = 1.5yy(0) = −1h = 0.2
y4 =
6.Hard
00.20.40.60.80.60.81ty(0, 1)

Use Euler's method with h = 0.2 for y′ = t − y, y(0) = 1 to estimate y4 ≈ y(0.8).

y′ = t − yy(0) = 1h = 0.2
y4 =

Answer key

  1. 1. x2 = 2.926
  2. 2. x2 = 1.636
  3. 3. T = 1.114
  4. 4. S = 0.6378
  5. 5. y4 = −2.856
  6. 6. y4 = 0.6192

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