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• Cost and profit functions

Calculate the marginal and average cost for a given cost function.Find the corresponding startup/shutdown price.
Maximize the profit function at a given price.

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• SageMath Cell

Uses an extension to embed SageMath cells into content areas.

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• MATH6058 Factorising Quadratic Equations with $x^2$ Coefficients of 1

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

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• MATH6058 Algebraic fractions: operations involving algebraic fractions

Add, subtract, multiply and divide algebraic fractions.

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• Blathnaid's copy of Simplify logarithms

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$

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• Algebra: Completing the square

Several quadratics are given and students are asked to complete the square.

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• Integration revision

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

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• Frame: A-Frame with load

Solve for the internal forces at on a multipart frame.

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• Area under a curve by integration

Find roots and the area under a parabola

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• 01 - Complex Numbers | Exercises

Self-assessment questions. Solve 50% of the available marks to pass this exercise.

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