Continuity formulas

Every formula JEE Advanced expects you to know for Continuity, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

Practise these formulas 129 practice questions

Formulas: 26
Subject: Mathematics
Exam: JEE Advanced
No sign-in needed: ₹0

Continuity, every formula

26 formulas, typeset and free. Print it, or keep it open beside your practice.

Continuity at a point
$x \to a lim f (x) = f (a)$
Three conditions
$f (a) defined, x \to a lim f exists, x \to a lim f = f (a)$
Left continuity
$x \to a^{-} lim f (x) = f (a)$
Right continuity
$x \to a^{+} lim f (x) = f (a)$
Continuity on [a,b]
$cts on (a, b), right-cts at a, left-cts at b$
Sum/difference continuous
$f \pm g continuous at a$
if f,g continuous at a
Product continuous
$f \cdot g continuous at a$
Scalar multiple continuous
$c f continuous at a, c \in R$
Quotient continuous
$\frac{f}{g} continuous at a if g (a) \neq = 0$
Composite continuous
$f cts at a, g cts at f (a) \Rightarrow g \circ f cts at a$
Discontinuity
$f not continuous at a \Rightarrow f discontinuous at a$
Removable discontinuity
$x \to a lim f exists but \neq = f (a) (or f (a) undefined)$
Missing-point discontinuity
$x \to a lim f exists, f (a) undefined$
Isolated-point discontinuity
$x \to a lim f exists, f (a) defined, lim \neq = f (a)$
Jump (finite) discontinuity
$x \to a^{-} lim f, x \to a^{+} lim f finite but unequal$
Jump of discontinuity
$x \to a^{+} lim f - x \to a^{-} lim f$
Infinite discontinuity
$at least one one-sided limit = \pm \infty$
Oscillatory discontinuity
$limit oscillates between finite values (e.g. sin \frac{1}{x})$
Continuity of elementary functions
$polynomials, sin, cos, e^{x}, lo g cts on their domains$
Boundedness on [a,b]
$f cts on [a, b] \Rightarrow k \leq f (x) \leq m$
attains min k, max m
Intermediate value theorem
$f cts on [a, b], y_{0} between f (a), f (b) \Rightarrow f (c) = y_{0}$
Root existence (IVT)
$f (a) f (b) < 0 \Rightarrow f (c) = 0 for some c \in (a, b)$
Attains every value in [k,m]
$range of a continuous f on [a, b] is [k, m]$
|f| continuity
$f cts \Rightarrow ∣ f ∣ cts (converse false)$
Redefining to remove discontinuity
$set f (a) = x \to a lim f (x)$
Single-point continuity
$a function may be continuous at only one point$

Know the Continuity formulas. Now use them.

Formulas only stick when you apply them under time. Adaptive practice picks the concept you keep dropping marks on.

Create a free account All formula sheets

Join QuestPix, Today!

Get notified first, with exam & curriculum updates, course & test series launch offers, motivation & success stories and free learning resources recommended by toppers.

Continuity formulas

Continuity, every formula

Continuity at a point

Three conditions

Left continuity

Right continuity

Continuity on [a,b]

Sum/difference continuous

Product continuous

Scalar multiple continuous

Quotient continuous

Composite continuous

Discontinuity

Removable discontinuity

Missing-point discontinuity

Isolated-point discontinuity

Jump (finite) discontinuity

Jump of discontinuity

Infinite discontinuity

Oscillatory discontinuity

Continuity of elementary functions

Boundedness on [a,b]

Intermediate value theorem

Root existence (IVT)

Attains every value in [k,m]

|f| continuity

Redefining to remove discontinuity

Single-point continuity

More JEE Advanced Mathematics formula sheets

Know the Continuity formulas. Now use them.

Join QuestPix, Today!