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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... 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

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

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

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