CBSE Class 12 Maths Chapter 5 Continuity and Differentiability Formulas, Definitions and Theorems

CBSE 12th Maths Continuity and Differentiability Formulas: Check here for all the important formulas of mathematics in Chapter 5 Continuity and Differentiability of Class 12, along with major definitions and examples.

Maths Continuity and Differentiability Formulas: Calculus comprises nearly half of the curriculum of the CBSE class 12 mathematics syllabus. Chapter 5 Continuity and Differentiability is one of the biggest and most important chapters in class 12. It also consists of several high-level problems and advanced concepts.

Students need to master Continuity and Differentiability as not only is it important from an exam point of view but also essential for other calculus chapters in class 12 and in higher studies.

Calculus is a math concept that has troubled students and mathematicians alike. As such, many formulas, equations and theorems have been devised to simplify problems. Here at Jagran Josh, we cover all the necessary formulas of continuity and differentiability.

Not using formulas or other means to simplify problems makes them exponentially more challenging as you’ll notice if you forget any while solving questions. On that note, be sure to check out the CBSE Class 12 Maths Chapter 5 Continuity and Differentiability Formulas below.

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CBSE Class 12 Maths Chapter 5 Continuity and Differentiability Formulas and Theorems

We have listed all the important formulas, definitions and theorems of CBSE Class 12 Continuity and Differentiability here.

Continuity

A real valued function is continuous at a point in its domain if the limit of the function at that point equals the value of the function at that point. A function

is continuous if it is continuous on the whole of its domain.

Definitions of Continuity:-

-> At a point

Suppose ƒ is a real function on a subset of the real numbers and let c be

a point in the domain of f. Then ƒ is continuous at c if

-> Of a Real Function

A real function ƒ is said to be continuous if it is continuous at every point

in the domain of ƒ.

Upon further elaboration, we get

Suppose ƒ is a function defined on a closed interval [a, b], then for ƒ to be continuous, it needs to be continuous at every point in [a, b] including the endpoints a and b. Continuity of ƒ at a means

and continuity of ƒ at b means

Algebra of Continuous Functions

Suppose ƒ and g be two real functions continuous at a real number c.

Then,

(1) ƒ + g is continuous at x = c.

(2) ƒ – g is continuous at x = c.

(3) ƒ . g is continuous at x = c.

(4) ƒ/g is continuous at x = c, (provided g (c) ≠ 0).

Differentiability

A function ƒ is said to be differentiable at a point in its domain, if its left hand & right hand derivatives exist at c & are equal.

– Assume that if ƒ is a real function and c is a point in its domain. The derivative of ƒ at c is defined by 0

The derivative of a function ƒ at c is defined by-

*All differentiable functions are continuous but not vice versa.

Chain Rule:

Let f be a real-valued function which is a composite of two functions u and v; i.e., ƒ = v o u.

Suppose t = u(x) and if both dt/dx and dv/dt exist then,

dƒ/dx = (dv/dt). (dt/dx)

Standard Limits:

Standard Derivatives:

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