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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.
Celine deposited $505 into her savings account. If the interest rate of the account is 5% per year, how much interest will she have made after 4 years? Use the formula F = 9/5
1. Consider the following differential equation with initial conditions: t 2 x'' + 5 t x' + 3 x = 0, x(1) = 3, x'(1) = -13. Assume there is a solution of the form: x (t) = t
Write a function that computes the product of two matrices, one of size m × n, and the other of size n × p. Test your function in a program that passes the following two matrices t
(8-)
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find the area of the irregular shape 2cm 4cm 4cm 2cm 5cm 5cm
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