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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...
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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...
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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...
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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
...
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JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9430
Examine the continuity of the function at . Answer: R.H.L =
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JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9431
Examine the following function for continuity:
Answer: Let
Let ‘a’ be a ...
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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
...
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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...
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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
=
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JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9438
Is the function defined by continuous at Answer: At
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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 ...
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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
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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
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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
=
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JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9448
Find
in the following:
Answer: We are given that
…..(i) Differentiating (...
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JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9449
Find
in the following:
Answer: We are given that
…..(i) Differentiating (...
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JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9450
Find
in the following:
Answer: We are given that
……….(i) Di...
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JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9451
Find
in the following:
. Answer: We are given that
where
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JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9452
Differentiate w.r.t x:
Answer: Let
...
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JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9453
Differentiate w.r.t x:
Answer: Let
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JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9454
Differentiate w.r.t x:
Answer: Let
=
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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 &...
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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,
………(...
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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) ...
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JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9459
Find the second order derivative of the function:
Answer: Let
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JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9460
Find the second order derivative of the function:
Answer: Let
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JEE-Main - Grade 12 - Mathematics - Continuity and Differentiability - Study ref# 9461
Find the second order derivative of the function:
Answer: Let
 ...
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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)
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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)
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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)
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