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###
**Exercise 5.1 : ** Solutions of Questions on Page Number : **159**

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**Exercise 5.2 : ** Solutions of Questions on Page Number : **166**

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**Exercise 5.3 : ** Solutions of Questions on Page Number : **169**

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**Exercise 5.4 : ** Solutions of Questions on Page Number : **174**

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**Exercise 5.5 : ** Solutions of Questions on Page Number : **178**

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**Exercise 5.6 : ** Solutions of Questions on Page Number : **181**

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**Exercise 5.7 : ** Solutions of Questions on Page Number : **183**

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**Exercise 5.8 : ** Solutions of Questions on Page Number : **186**

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**Exercise Miscellaneous : ** Solutions of Questions on Page Number : **191**

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**Popular Articles**

Q1 :
**
**

Prove that the functionis continuous at

**Answer :**

Therefore, *f* is continuous
at *x*= 0

Therefore, *f* is continuous
at *x*=
- 3

Therefore, *f* is continuous
at *x*= 5

Answer needs Correction? Click Here

Q2 :
**
**

Examine the continuity of the function.

**Answer :**

Thus, *f* is continuous
at *x*= 3

Answer needs Correction? Click Here

Q3 :
**
**

Examine the following functions for continuity.

(a) (b)

(c) (d)

**Answer :**

Q4 :
**
**

Prove that the function is continuous at
*x*= *n*,
where *n* is a positive
integer.

**Answer :**

Q5 :
**
**

Is the function *f*defined
by

continuous at
*x*= 0? At
*x*= 1? At
*x*= 2?

**Answer :**

Q6 :
**
**

Find all points of discontinuity of
*f*, where *f*
is defined by

**Answer :**

Q7 :
**
**

Find all points of discontinuity of
*f*, where *f*
is defined by

**Answer :**

Q8 :
**
**

Find all points of discontinuity of
*f*, where *f*
is defined by

**Answer :**

Q9 :
**
**

Find all points of discontinuity of
*f*, where *f*
is defined by

**Answer :**

Q10 :
**
**

Find all points of discontinuity of
*f*, where *f*
is defined by

**Answer :**

Q11 :
**
**

Find all points of discontinuity of
*f*, where *f*
is defined by

**Answer :**

Q12 :
**
**

Find all points of discontinuity of
*f*, where *f*
is defined by

**Answer :**

Q13 :
**
**

Is the function defined by

a continuous function?

**Answer :**

Q14 :
**
**

Discuss the continuity of the function
*f*, where *f*
is defined by

**Answer :**

Q15 :
**
**

Discuss the continuity of the function
*f*, where *f*
is defined by

**Answer :**

Q16 :
**
**

Discuss the continuity of the function
*f*, where *f*
is defined by

**Answer :**

Q17 :
**
**

Find the relationship between
*a*and *b*
so that the function
*f*defined by

is continuous at *x* =
3.

**Answer :**

Q18 :
**
**

For what value of is the function defined by

continuous at *x* = 0? What
about continuity at *x*= 1?

**Answer :**

Q19 :
**
**

Show that the function defined by is discontinuous at all
integral point. Here denotes the greatest
integer less than or equal to
*x*.

**Answer :**

Q20 :
**
**

Is the function defined by continuous at *x* =

**Answer :**

Q21 :
**
**

Discuss the continuity of the following functions.

(a)
*f*(*x*) =
sin *x* + cos
*x*

(b)
*f*(*x*) =
sin *x*
- cos
*x*

(c)
*f*(*x*) =
sin *x*
x cos x

**Answer :**

Q22 :
**
**

Discuss the continuity of the cosine, cosecant, secant and cotangent functions,

**Answer :**

Q23 :
**
**

Find the points of discontinuity of
*f*, where

**Answer :**

Q24 :
**
**

Determine if *f*defined
by

is a continuous function?

**Answer :**

Q25 :
**
**

Examine the continuity of
*f*, where *f*
is defined by

**Answer :**

Q26 :
**
**

Find the values of *k* so
that the function *f*is continuous
at the indicated point.

**Answer :**

Q27 :
**
**

Find the values of *k* so
that the function *f*is continuous
at the indicated point.

**Answer :**

Q28 :
**
**

Find the values of *k* so
that the function *f*is continuous
at the indicated point.

**Answer :**

Q29 :
**
**

Find the values of *k* so
that the function *f*is continuous
at the indicated point.

**Answer :**

Q30 :
**
**

Find the values of
*a*and *b*
such that the function defined by

is a continuous function.

**Answer :**

Q31 :
**
**

Show that the function defined by
*f* (*x*)
= cos
(*x*^{2}) is
a continuous function.

**Answer :**

Q32 :
**
**

Show that the function defined by is a continuous function.

**Answer :**

Q33 :
**
**

Examine that is a continuous function.

**Answer :**

Q34 :
**
**

Find all the points of discontinuity of
*f* defined by.

**Answer :**

Q1 :
**
**

Differentiate the functions with respect to *x*.

**Answer :**

Q2 :
**
**

Differentiate the functions with respect to *x*.

**Answer :**

Q3 :
**
**

Differentiate the functions with respect to *x*.

**Answer :**

Q4 :
**
**

Differentiate the functions with respect to *x*.

**Answer :**

Q5 :
**
**

Differentiate the functions with respect to *x*.

**Answer :**

Q6 :
**
**

Differentiate the functions with respect to *x*.

**Answer :**

Q7 :
**
**

Differentiate the functions with respect to *x*.

**Answer :**

Q8 :
**
**

Differentiate the functions with respect to *x*.

**Answer :**

Q9 :
**
**

Prove that the function *f* given by

is notdifferentiable
at *x* = 1.

**Answer :**

Q10 :
**
**

Prove that the greatest integer function defined byis not

differentiable at *x* = 1 and *x* = 2.

**Answer :**

Q1 :
**
**

Differentiate the following w.r.t. *x*:

**Answer :**

Q2 :
**
**

Differentiate the following w.r.t. *x*:

**Answer :**

Q3 :
**
**

Differentiate the following w.r.t. *x*:

**Answer :**

Q4 :
**
**

Differentiate the following w.r.t. *x*:

**Answer :**

Q5 :
**
**

Differentiate the following w.r.t. *x*:

**Answer :**

Q6 :
**
**

Differentiate the following w.r.t. *x*:

**Answer :**

Q7 :
**
**

Differentiate the following w.r.t. *x*:

**Answer :**

Q8 :
**
**

Differentiate the following w.r.t. *x*:

**Answer :**

Q9 :
**
**

Differentiate the following w.r.t. *x*:

**Answer :**

Q10 :
**
**

Differentiate the following w.r.t. *x*:

**Answer :**

Q1 :
**
**

Differentiate the function with respect to *x*.

**Answer :**

Q2 :
**
**

Differentiate the function with respect to *x*.

**Answer :**

Q3 :
**
**

Differentiate the function with respect to *x*.

**Answer :**

Q4 :
**
**

Differentiate the function with respect to *x*.

**Answer :**

Q5 :
**
**

Differentiate the function with respect to *x*.

**Answer :**

Q6 :
**
**

Differentiate the function with respect to *x*.

**Answer :**

Q7 :
**
**

Differentiate the function with respect to *x*.

**Answer :**

Q8 :
**
**

Differentiate the function with respect to *x*.

**Answer :**

Q9 :
**
**

Differentiate the function with respect to *x*.

**Answer :**

Q10 :
**
**

Differentiate the function with respect to *x*.

**Answer :**

Q11 :
**
**

Differentiate the function with respect to *x*.

**Answer :**

Q12 :
**
**

Find of function.

**Answer :**

Q13 :
**
**

Find of function.

**Answer :**

Q14 :
**
**

Find of function.

**Answer :**

Q15 :
**
**

Find of function.

**Answer :**

Q16 :
**
**

Find the derivative of the function given by and hence find.

**Answer :**

Q17 :
**
**

Differentiate in three ways mentioned below

(i) By using product rule.

(ii) By expanding the product to obtain a single polynomial.

(iii By logarithmic differentiation.

Do they all give the same answer?

**Answer :**

Q18 :
**
**

If *u*, *v* and *w* are functions of *x*,
then show that

in two ways-first by repeated application of product rule, second by logarithmic differentiation.

**Answer :**

Q1 :
**
**

If *x* and *y* are connected parametrically by the
equation, without eliminating the parameter, find.

**Answer :**

Q2 :
**
**

If *x* and *y* are connected parametrically by the
equation, without eliminating the parameter, find.

*x* = *a* cos *θ*, *y*
= *b* cos *θ*

**Answer :**

Q3 :
**
**

If *x* and *y* are connected parametrically by the
equation, without eliminating the parameter, find.

*x* = sin *t*, *y* = cos 2*t*

**Answer :**

Q4 :
**
**

If *x* and *y* are connected parametrically by the
equation, without eliminating the parameter, find.

**Answer :**

Q5 :
**
**

If *x* and *y* are connected parametrically by the
equation, without eliminating the parameter, find.

**Answer :**

Q6 :
**
**

If *x* and *y* are connected parametrically by the
equation, without eliminating the parameter, find.

**Answer :**

Q7 :
**
**

If *x* and *y* are connected parametrically by the
equation, without eliminating the parameter, find.

**Answer :**

Q8 :
**
**

If *x* and *y* are connected parametrically by the
equation, without eliminating the parameter, find.

**Answer :**

Q9 :
**
**

If *x* and *y* are connected parametrically by the
equation, without eliminating the parameter, find.

**Answer :**

Q10 :
**
**

If *x* and *y* are connected parametrically by the
equation, without eliminating the parameter, find.

**Answer :**

Q1 :
**
**

Find the second order derivatives of the function.

**Answer :**

Q2 :
**
**

Find the second order derivatives of the function.

**Answer :**

Q3 :
**
**

Find the second order derivatives of the function.

**Answer :**

Q4 :
**
**

Find the second order derivatives of the function.

**Answer :**

Q5 :
**
**

Find the second order derivatives of the function.

**Answer :**

Q6 :
**
**

Find the second order derivatives of the function.

**Answer :**

Q7 :
**
**

Find the second order derivatives of the function.

**Answer :**

Q8 :
**
**

Find the second order derivatives of the function.

**Answer :**

Q9 :
**
**

Find the second order derivatives of the function.

**Answer :**

Q10 :
**
**

Find the second order derivatives of the function.

**Answer :**

Q12 :
**
**

If findin terms of *y*
alone.

**Answer :**

Q1 :
**
**

Verify Rolle's Theorem for the function

**Answer :**

Q2 :
**
**

Examine if Rolle's Theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle's Theorem from these examples?

(i)

(ii)

(iii)

**Answer :**

Q3 :
**
**

If is a differentiable function and if does not vanish anywhere, then prove that.

**Answer :**

Q4 :
**
**

Verify Mean Value Theorem, if in the interval, where and.

**Answer :**

Q5 :
**
**

Verify Mean Value Theorem, if in the interval
[*a*, *b*], where *a* = 1 and *b* = 3. Find
all for which

**Answer :**

Q6 :
**
**

Examine the applicability of Mean Value Theorem for all three functions given in the above exercise 2.

**Answer :**

Q8 :
**
**

**,**
for some constant
*a*and
*b*.

**Answer :**

Q10 :
**
**

, for some fixed and

**Answer :**

Q14 :
**
**

If, for,
- 1 <
*x*<1, prove that

**Answer :**

Q15 :
**
**

If, for some prove that

is a constant
independent of *a*and
*b*.

**Answer :**

Q16 :
**
**

If with prove that

**Answer :**

Q18 :
**
**

If, show that
exists for all
real *x*, and find it.

**Answer :**

Q19 :
**
**

Using mathematical induction prove that
for all positive
integers *n*.

**Answer :**

Q20 :
**
**

Using the fact that sin (*A*
+ *B*) = sin
*A*cos *B*
+ cos *A* sin
*B* and the differentiation, obtain the
sum formula for cosines.

**Answer :**

Q21 :
**
Does there exist a function which is continuos everywhere but not
differentiable at exactly two points? Justify your answer ? **

**Answer :**

Maths Part-1 - Maths : CBSE ** NCERT ** Exercise Solutions for Class 12th for ** Continuity and Differentiability ** ( Exercise 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

- 12th Maths Paper Solutions Set 1 : CBSE Delhi Previous Year 2015
- 12th Maths Paper Solutions Set 2 : CBSE Delhi Previous Year 2015
- 12th Maths Paper Solutions Set 3 : CBSE Delhi Previous Year 2015

- 12th Maths Paper Solutions Set 1 : CBSE Abroad Previous Year 2014
- 12th Maths Paper Solutions Set 1 : CBSE All India Previous Year 2014
- 12th Maths Paper Solutions Set 1 : CBSE Delhi Previous Year 2014

- 12th Maths Paper Solutions Set 1 : CBSE All India Previous Year 2013

- Maths Part-1 : Chapter 6 - Application of Derivatives Class 12
- Maths Part-2 : Chapter 7 - Integrals Class 12
- Maths Part-1 : Chapter 1 - Relations and Functions Class 12
- Maths Part-1 : Chapter 3 - Matrices Class 12
- Maths Part-1 : Chapter 4 - Determinants Class 12
- Maths Part-1 : Chapter 2 - Inverse Trigonometric Functions Class 12
- Maths Part-2 : Chapter 13 - Probability Class 12
- Maths Part-2 : Chapter 8 - Application of Integrals Class 12
- Maths Part-2 : Chapter 9 - Differential Equations Class 12

Exercise 5.2 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Exercise 5.3 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Question 11 |

Question 12 |

Question 13 |

Question 14 |

Question 15 |

Exercise 5.4 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Exercise 5.6 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Question 11 |

Exercise 5.8 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |