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Next Chapter 14 : Mathematical Reasoning >>

###
**Exercise 13.1 : ** Solutions of Questions on Page Number : **301**

<< Previous Chapter 12 : Introduction to Three Dimensional Geometry
Next Chapter 14 : Mathematical Reasoning >>
###
**Exercise 13.2 : ** Solutions of Questions on Page Number : **312**

<< Previous Chapter 12 : Introduction to Three Dimensional Geometry
Next Chapter 14 : Mathematical Reasoning >>
###
**Exercise Miscellaneous : ** Solutions of Questions on Page Number : **317**

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Next Chapter 14 : Mathematical Reasoning >>
**Popular Articles**

Q3 :
**
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Evaluate the Given limit:

**Answer :**

Q4 :
**
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Evaluate the Given limit:

**Answer :**

Q5 :
**
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Evaluate the Given limit:

**Answer :**

Q6 :
**
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Evaluate the Given limit:

**Answer :**

Q7 :
**
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Evaluate the Given limit:

**Answer :**

Q8 :
**
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Evaluate the Given limit:

**Answer :**

Q9 :
**
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Evaluate the Given limit:

**Answer :**

Q10 :
**
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Evaluate the Given limit:

**Answer :**

Q11 :
**
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Evaluate the Given limit:

**Answer :**

Q12 :
**
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Evaluate the Given limit:

**Answer :**

Q13 :
**
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Evaluate the Given limit:

**Answer :**

Q14 :
**
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Evaluate the Given limit:

**Answer :**

Q15 :
**
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Evaluate the Given limit:

**Answer :**

Q16 :
**
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Evaluate the given limit:

**Answer :**

Q17 :
**
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Evaluate the Given limit:

**Answer :**

Q18 :
**
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Evaluate the Given limit:

**Answer :**

Q19 :
**
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Evaluate the Given limit:

**Answer :**

Q20 :
**
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Evaluate the Given limit:

**Answer :**

Q21 :
**
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Evaluate the Given limit:

**Answer :**

Q23 :
**
**

Find *f*(*x*)
and*f*(*x*),
where *f*(*x*) =

**Answer :**

Q24 :
**
**

Find *f*(*x*),
where *f*(*x*) =

**Answer :**

Q25 :
**
**

Evaluate*f*(*x*),
where *f*(*x*) =

**Answer :**

Q26 :
**
**

Find*f*(*x*),
where *f*(*x*) =

**Answer :**

Q27 :
**
**

Find*f*(*x*),
where *f*(*x*) =

**Answer :**

Q28 :
**
**

Suppose *f*(*x*) = and if*f*(*x*) = *f*(1) what are possible values of
*a* and *b*?

**Answer :**

Q29 :
**
**

Letbe fixed real numbers and define a function

What is*f*(*x*)? For
some compute*f*(*x*).

**Answer :**

Q30 :
**
**

If *f*(*x*) =.

For what value (s) of a does *f*(*x*) exists?

**Answer :**

Q31 :
**
**

If the function *f*(*x*) satisfies, evaluate.

**Answer :**

Q32 :
**
**

If. For what integers
*m* and *n* does and exist?

**Answer :**

Q1 :
**
**

Find the derivative of *x*^{2} -
2 at *x* = 10.

**Answer :**

Q2 :
**
**

Find the derivative of 99*x* at *x* = 100.

**Answer :**

Q3 :
**
**

Find the derivative of *x* at *x* = 1.

**Answer :**

Q4 :
**
**

Find the derivative of the following functions from first principle.

(i) *x*^{3} â€“ 27 (ii) (*x*
â€“ 1) (*x* â€“ 2)

(ii) (iv)

**Answer :**

Q5 :
**
**

For the function

Prove that

**Answer :**

Q6 :
**
**

Find the derivative offor some fixed real
number *a*.

**Answer :**

Q7 :
**
**

For some constants *a* and *b*, find the derivative of

(i) (*x* â€“ *a*) (*x*
â€“ *b*) (ii) (*ax*^{2} +
*b*)^{2} (iii)

**Answer :**

Q8 :
**
**

Find the derivative offor some constant
*a*.

**Answer :**

Q9 :
**
**

Find the derivative of

(i) (ii)
(5*x*^{3} + 3*x* â€“ 1)
(*x* â€“ 1)

(iii) *x*^{â€“3} (5 + 3*x*)
(iv) *x*^{5} (3 â€“
6*x*^{â€“9})

(v) *x*^{â€“4} (3
â€“ 4*x*^{â€“5})
(vi)

**Answer :**

Q10 :
**
**

Find the derivative of cos *x* from first principle.

**Answer :**

Q11 :
**
**

Find the derivative of the following functions:

(i) sin *x* cos *x* (ii) sec *x* (iii) 5 sec
*x* + 4 cos *x*

(iv) cosec *x* (v) 3cot *x* + 5cosec *x*

(vi) 5sin *x* - 6cos *x* + 7 (vii)
2tan *x* - 7sec *x*

**Answer :**

Q1 :
**
**

Find the derivative of the following functions from first principle:

(i) â€“*x* (ii)
(â€“*x*)^{â€“1}
(iii) sin (*x* + 1)

(iv)

**Answer :**

Q2 :
**
**

Find the derivative of the following functions (it is to be
understood that *a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers): (*x* + *a*)

**Answer :**

Q3 :
**
**

Find the derivative of the following functions (it is to be
understood that *a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Q4 :
**
**

Find the derivative of the following functions (it is to be
understood that *a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers): (*ax* + *b*)
(*cx* + *d*)^{2}

**Answer :**

Q5 :
**
**

Find the derivative of the following functions (it is to be
understood that *a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Q6 :
**
**

Find the derivative of the following functions (it is to be
understood that *a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Q7 :
**
**

*a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Q8 :
**
**

*a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Q9 :
**
**

*a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Q10 :
**
**

*a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Q11 :
**
**

*a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Q12 :
**
**

Find the derivative of the following functions (it is to be
understood that *a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers): (*ax* +
*b*)^{n}

**Answer :**

Q13 :
**
**

Find the derivative of the following functions (it is to be
understood that *a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers): (*ax* +
*b*)^{n} (*cx* +
*d*)^{m}

**Answer :**

Q14 :
**
**

Find the derivative of the following functions (it is to be
understood that *a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers): sin (*x* + *a*)

**Answer :**

Q15 :
**
**

Find the derivative of the following functions (it is to be
understood that *a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers): cosec *x* cot *x*

**Answer :**

Q16 :
**
**

*a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Q17 :
**
**

*a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Q18 :
**
**

*a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Q19 :
**
**

Find the derivative of the following functions (it is to be
understood that *a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers): sin^{n}
*x*

**Answer :**

Q20 :
**
**

*a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Q21 :
**
**

*a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Q22 :
**
**

Find the derivative of the following functions (it is to be
understood that *a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers): *x*^{4} (5 sin
*x* - 3 cos *x*)

**Answer :**

Q23 :
**
**

Find the derivative of the following functions (it is to be
understood that *a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers): (*x*^{2} + 1)
cos *x*

**Answer :**

Q24 :
**
**

Find the derivative of the following functions (it is to be
understood that *a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers): (*ax*^{2} + sin
*x*) (*p* + *q* cos *x*)

**Answer :**

Q25 :
**
**

*a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Q26 :
**
**

*a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Q27 :
**
**

*a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Q28 :
**
**

*a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Q29 :
**
**

Find the derivative of the following functions (it is to be
understood that *a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers): (*x* + sec *x*)
(*x* - tan *x*)

**Answer :**

Q30 :
**
**

*a*, *b*, *c*, *d*, *p*,
q, *r* and *s* are fixed non-zero constants and
*m* and *n* are integers):

**Answer :**

Maths - Maths : CBSE ** NCERT ** Exercise Solutions for Class 11th for ** Limits and Derivatives ** ( Exercise 13.1, 13.2, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

- Maths : Chapter 3 - Trigonometric Functions Class 11
- Maths : Chapter 4 - Principle of Mathematical Induction Class 11
- Maths : Chapter 5 - Complex Numbers and Quadratic Equations Class 11
- Maths : Chapter 2 - Relations and Functions Class 11
- Maths : Chapter 1 - Sets Class 11
- Maths : Chapter 9 - Sequences and Series Class 11
- Maths : Chapter 6 - Linear Inequalities Class 11
- Maths : Chapter 7 - Permutations and Combinations Class 11
- Maths : Chapter 8 - Binomial Theorem Class 11

Exercise 13.2 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Question 11 |