Why is index notation useful?
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what are indices in maths Informational
- Using the definition of repeated multiplication. Using mathematical induction for integer exponents. How does the concept of indices relate to the fundamental theorem of algebra? How are indices used in the definition of eigenvalues and eigenvectors of a matrix? How are indices used in the theory of Lie groups and Lie algebras? What are some connections between indices and other areas of mathematics that we haven't discussed yet?
- How are indices related to logarithms?
- Rewrite $\frac{1}{5^2}$ using a negative index.
- Graph $y = (1/2)^x$. Graph $y = 2^{x+1}$.
- Calculus of exponential and logarithmic functions.
- Solve for x $4^x = \frac{1}{16}$. Solve for x $9^{x/2} = 27$.
- What is the general shape of the graph of $y = a^x$ where $a > 1$?
- Solve for x and y $2^x = 4^y$ and $3^{x+y} = 27$.
- Solve for x $(\sqrt{2})^x = 4$. What are the common mistakes people make when working with indices?
- 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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