UNIT:8 Limit, Continuity & Differentiability
- Real – valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions.
- Graphs of simple functions.
- Limits, continuity, and differentiability.
- Differentiation of the sum, difference, product, and quotient of two functions.
- Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order up to two.
- Rolle's and Lagrange's Mean Value Theorems.
- Applications of derivatives: Rate of change of quantities, monotonic – increasing and decreasing functions, Maxima, and minima of functions of one variable, tangents, and normals.