What is the concept of continuity in NCERT Class 12 Chapter 5?

<p>The concept of continuity is defined for a function&nbsp; as a curve that is smooth and unbroken at every point in its domain. Mathematically, a function <math ><semantics><mrow><mi>f</mi><mo stretchy="false"> (</mo><mi>x</mi><mo stretchy="false">)</mo></mrow>&lt;annotation encoding="application/x-tex"&gt;f (x)</annotation></semantics></math> is said to be continuous at a point <math ><semantics><mrow><mi>x</mi><mo>=</mo><mi>a</mi></mrow>&lt;annotation encoding="application/x-tex"&gt;x = a</annotation></semantics></math> if:</p><p><math ><semantics><mrow><munder><mrow><mi>lim</mi><mo>? </mo></mrow><mrow><mi>x</mi><mo>? </mo><mi>a</mi></mrow></munder><mi>f</mi><mo stretchy="false"> (</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mi>f</mi><mo stretchy="false"> (</mo><mi>a</mi><mo stretchy="false">)</mo></mrow>&lt;annotation encoding="application/x-tex"&gt;\lim_ {x \to a} f (x) = f (a)</annotation></semantics></math></p><p>What it means:</p><ul><li><p>The function is defined at <math ><semantics><mrow><mi>x</mi><mo>=</mo><mi>a</mi></mrow>&lt;annotation encoding="application/x-tex"&gt;x = a</annotation></semantics></math>, </p></li><li><p>The limit of the function exists as <math ><semantics><mrow><mi>x</mi></mrow>&lt;annotation encoding="application/x-tex"&gt;x</annotation></semantics></math> approaches <math ><semantics><mrow><mi>a</mi></mrow>&lt;annotation encoding="application/x-tex"&gt;a</annotation></semantics></math>, </p></li><li><p>And the limit is equal to the function's value at that point.</p></li></ul><p>Students can check the <strong>NCERT Class 12 Maths Chapter 5 Continuity and Differentiability</strong>&nbsp;for better and deep understanding of the topic.</p>

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