Continuity makes a graph unbroken; differentiability makes it smooth. This course tests both and develops every standard differentiation technique.
The course follows the NCERT Class 12 Mathematics chapter Continuity and Differentiability and has 3 lessons. Each lesson explains the ideas with worked examples and ends with practice questions and full answers. The numbers in every example and question are our own, so the lessons can be used alongside the textbook exercises.
- Continuity and Differentiability — Continuity at a point, piecewise functions, finding constants for continuity, and the link between continuity and differentiability.
- Techniques of Differentiation — Chain rule, derivatives of inverse trigonometric, exponential and log functions, implicit, logarithmic and parametric differentiation, second derivatives.
- Continuity and Differentiability: Mixed Practice — Twelve questions on continuity and differentiation techniques, with answers.
By the end you will be able to:
- Test continuity of piecewise functions.
- Relate continuity and differentiability.
- Differentiate with the chain rule and standard derivatives.
- Use implicit, logarithmic and parametric differentiation.