Course: Pre-Calculus (4431) Semester: Spring, 2024
ASSIGNMENT No. 1
(Units: 1–4)
Q. 1 (a) For each of the following statements, either prove it is true or give counter example to show it is false;
- The product of two rational numbers is always rational
- The product of two rational numbers is always irrational.
- The product of a non-zero rational and an irrational is always irrational.
- The product of two irrational numbers is always rational
(b) Prove that if n is any positive integer, then + is irrational.
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Q. 2 (a) Determine whether the following functions are even or odd:
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(b) Given that f (x) = 2x + 1 and h(x) = 2x2 + 4x + 1 find a function g such that, f(g(x)) = h(x)
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Q. 3 (a) Find all values of a such that
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(b) Approximate the value for the following limit. Confirm your approximation using graphical evidence.
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