Generating functions use powers of a variable to encode sequences. How are indices used in probability distributions (e.g., binomial distribution, Poisson distribution)?
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what are indices in maths Informational
- Solve for x $(\frac{1}{2})^x = 8$.
- What is the power rule for differentiation?
- Solve for x $10^x = 10000$. Solve for x $e^x = e^3$.
- Solve for x $(0.5)^x = 0.125$.
- Powers of 10 represent different orders of magnitude. How can you use indices to compare the relative sizes of very large or very small numbers? How are indices used in computer storage units (e.g., bits, bytes, kilobytes, etc.)?
- What is the limit of $a^x$ as $x \to -\infty$ for $a > 1$? What is the limit of $a^x$ as $x \to \infty$ for $0 < a < 1$?
- When multiplying powers with the same base, what do you do with the exponents? What is the second law of indices?
- Can the base be 1?
- How are indices used in binary numbers?
- Extremely important as it forms the basis for many other topics. Understanding indices is crucial for advanced mathematical studies and applications.
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