The 5th chapter present in the class 12th syllabus, is titled as Continuity and Differentiability. Continuity can simply be defined as the function, which causes small changes in the input which leads to small changes in the output as well. Differentiability, on the other hand, can be defined as the function that is differentiable at a point, existing at every point in its domain. Another important concept that is taught to students in this chapter are the main reasons for discontinuity.The properties of continuous functions and the intermediate value theorem are also important concepts which are taught in this chapter. The list of continuous and differentiable functions are also present, which makes problem solving much simpler.
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Frequently asked Questions on CBSE Class 12 Maths Notes Chapter 5: Continuity and Differentiability
What does the ‘intermediate value theorem’ state?
In mathematical analysis, the intermediate value theorem states that if f is a continuous function whose domain contains the interval [a, b], then it takes on any given value between f(a) and f(b) at some point within the interval.
What does ‘Limit’ mean in mathematical terms?
In mathematics, a limit is the value that a function (sequence) approaches as the input (or index) approaches some value.
What is a ‘Differential Equation’?
A differential equation is a mathematical equation that involves variables like x or y, as well as the rate at which those variables change.