JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Introduction and Snapshot of Continuity and Differentiability - Study ref# 911

Introduction
We had learnt to differentiate certain
functions like polynomial functions and trigonometric functions. In this
chapter, we introduce the very important concepts of continuity,
differentiability and relations between them. We... read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Introduction and Snapshot of Continuity and Differentiability - Study ref# 912

Following sections must be covered to
understand the Continuity and Differentiability:
1. Continuity
2. Differentiability
3. Exponential and Logarithmic Function
4. Derivative of Functions in Parametric
Forms
5. Second Order D... read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Target Setup for Continuity and Differentiability - Study ref# 913

Student requires to achieve the following milestones to get better grip over Continuity and Differentiability. The milestones / targets are as follows: Starting Point: Days 0Test TypeAppear on TestTarget TestsScorePractice Test00... read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9429

Prove that the function is
continuous at t
and
at. Answer:
At
We have
... read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9430

Examine the continuity of the function at
. Answer: R.H.L = read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9431

Examine the following function for
continuity:
Answer: Let
Let ‘a’ be a ... read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9432

Is the function f defined by
continuous at At
At
Answer: (i) At function
polynomial
hence continuous.
For ... read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9434

Find all points of discontinuity of f,
where f is defined by
Answer: At Answer: We observe that is
continuous at all real number... read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9436

Discuss the continuity of the function f,
where f is defined by
Answer: At
= read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9438

Is the function defined by continuous
at Answer: At read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9439

Discuss the continuity of the following
functions :
(a) (b)
(c) Answer: (a) Let a be an arbitrary real number
... read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9440

Find the points of discontinuity of f,
where
Answer: At
L.H.L = Answer: Let read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9446

Prove that the function f given by is
not differentiable at Answer: We have
read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9447

Prove that the greatest integer function
defined by is
not differentiable at and
Answer: At
= read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9448

Find in
the following:
Answer: We are given that …..(i)
Differentiating (... read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9449

Find in
the following:
Answer: We are given that …..(i)
Differentiating (... read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9450

Find in
the following:
Answer: We are given that
……….(i)
Di... read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9451

Find in
the following:
. Answer: We are given that
where read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9452

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9453

Differentiate w.r.t x:
Answer: Let read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9454

Differentiate w.r.t x:
Answer: Let
= read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9455

Differentiate the function w.r.t x:
Answer: Let …..(i)
Taking log on both sides of (i), we get
Answer: Let where
and
&... read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9457

If x and y are connected parametrically
by the equations , without eliminating the parameter , Find .
Answer: Here, ………(... read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9458

If x and y are connected parametrically
by the equations , without eliminating the parameter , Find .
Answer: Here, ………(1)
... read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9459

Find the second order derivative of the
function:
Answer: Let read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9460

Find the second order derivative of the
function:
Answer: Let read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9461

Find the second order derivative of the
function:
Answer: Let ... read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9462

Examine if Rolle’s theorem is a
applicable to any of the following functions. Can you say something about the
converse of Rolle’s theorem from these examples?
(i) for
(ii) read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9463

Verify Mean Value Theorem, if in
the interval [a, b], where a =1 and b =3. Find all for
which . Answer: (i) Function is continuous in [1,3] as it
is a polynomial function and polynomial function is always continuous.
(ii) read more

JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9464

Examine the applicability of Mean Value
Theorem for all three functions:
(i) for
(ii) for
(iii) read more