Calculus of exponential and logarithmic functions.
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what are indices in maths Informational
- Groups, rings, and fields have notions of powers of elements. How are indices related to the concept of dimension in mathematics and physics?
- Rewrite $\frac{1}{5^2}$ using a negative index.
- Give an example of a polynomial with terms involving indices. How are indices used in calculus (e.g., differentiation and integration)?
- State the power of a power rule.
- If $y = a^x$, then $x = \log_a y$. How can you estimate the value of numbers raised to large powers?
- Simplify $\frac{(ab)^2}{a^2b^3}$. Simplify $(\frac{x^2y}{xy^3})^{-2}$.
- How do you apply the exponent to both the numerator and denominator of a fraction? What is a negative index?
- Fractional indices.
- How do you rationalize the denominator of a surd? Rationalize $\frac{1}{\sqrt{2}}$.
- Natural exponential function $e^x$ has important properties in calculus.
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