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I see you've uploaded a mathematics exam sheet with various questions on algebra, logarithms, matrix operations, limits, continuity, and calculus (differentiation). I'll provide detailed solutions and explanations for each question.

Could you specify which question you'd like me to start with, or would you prefer a walkthrough of the entire exam? 

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**Additional Questions for Practice:**

1. How would you solve similar problems involving logarithmic expressions?
2. What are the steps to check for continuity at a specific point in a piecewise function?
3. Can you find the differential of a product of three functions?
4. How do you simplify complex algebraic fractions with multiple variables?
5. What are the common logarithmic properties that simplify expressions?

**Tip:** When dealing with limits involving square roots, try to rationalize the expression by multiplying by the conjugate to simplify.

Solve the mathematical problems on the exam sheet provided.

Explore detailed solutions to university-level mathematics problems covering algebra, logarithmic expressions, matrix operations, limits, continuity, and differentiation. This comprehensive guide is ideal for first-year students studying introductory mathematics.

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