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ENG1005 - Engineering mathematics - MUM S2 2025
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Find a diagonalisation of the matrix .
You should write your solution on paper. In an exam scenario you would have time after the exam is finished to scan/photograph and upload your solution.
Consider the function given by(a) Find the maximum value of .(b) Use the method of Lagrange multipliers to find the maximum value of the function subject to the constraint .
You should write your solution on paper. In an exam scenario you would have time after the exam is finished to scan/photograph and upload your solution.
a) Using l'Hopital's rule, find the limit
b) Evaluate .
c) Find the value of the constant if satisfies
You should write your solution on paper. In an exam scenario you would have time after the exam is finished to scan/photograph and upload your solution.
A differential equation of the form
is called a Bernoulli differential equation. Note that this differential equation is linear for and , and nonlinear otherwise.
(a) Assuming that is not equal to or , show that satisfies the linear differential equation
(b) Use part (a) to solve the IVP
[Hint: You might find the identity useful.]
You should write your solution on paper. In an exam scenario you would have time after the exam is finished to scan/photograph and upload your solution.
Solve the differential equation with initial conditions and .
You should write your solution on paper. In an exam scenario you would have time after the exam is finished to scan/photograph and upload your solution.