Скачать или смотреть Class-12th|Maths| Ex-5.6| Ch-Continuity and Differentiability|NCERT Board exam 2026

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Core concepts and definitions Continuity:Definition: Understand the formal definition of a function \(f(x)\) being continuous at a point \(x=c\). A function is continuous at a point if the limit from the left, the limit from the right, and the function's value at that point are all finite and equal to each other.Graphical interpretation: Students should be able to recognize a continuous function from its graph—one that can be drawn without lifting the pen.Discontinuity: Identify the conditions under which a function is discontinuous at a point.Algebra of continuous functions: Understand that the sum, difference, product, and quotient of continuous functions are also continuous.Differentiability:Definition: Understand the definition of a function being differentiable at a point \(x=c\) if its derivative, \(f^{\prime }(c)\), exists. This is equivalent to the left-hand derivative and right-hand derivative being finite and equal.Geometrical meaning: Interpret the derivative as the slope of the tangent line to the function's graph at a particular point.Relationship with continuity: Comprehend the important theorem that every differentiable function is continuous, but a continuous function is not necessarily differentiable (e.g., \(f(x)=|x|\) at \(x=0\)).