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Consider the equation
ex3 + x2 - x - 6 = 0, e > 0 (1)
1. Apply a naive regular perturbation of the form
do derive a three-term approximation to the solutions of (1).
2. The above perturbation expansion should only give you an approximation for 2 of the roots.
Apply a leading order balance argument to device suitable expansions for the other root, again in the limit e ! 0+. Again, derive a three-term approximation this third case.
3. Solve (1) numerically for e = 0.01 (use Matlab or Maple or something). Use your three-term approximation for the three roots found in Q1 and 2 and provide the error (in terms of a percentage) in each case.
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sin3θ = cos2θ find the most general values of θ satisfying the equatios? sinax + cosbx = 0 solve ? Solution) sin (3x) = sin(2x + x) = sin(2x)cos(x) + cos(2x)sin(x) = 2sin(x)cos(
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#question.prove that the diagonals of a trapezium divide each other proportionally .
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