NCERT Solutions for Class 11 Maths Chapter 13- Limits and Derivatives

Exercise 13.1 page no: 301

1. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 1

Solution:

Given

NCERT Solutions Mathematics Class 11 Chapter 13 - 2

Substituting x = 3, we get

= 3 + 3

= 6

2. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 3

Solution:

Given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 4

Substituting x = π, we get

NCERT Solutions Mathematics Class 11 Chapter 13 - 5= (π – 22 / 7)

3. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 6

Solution:

Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 7

Substituting r = 1, we get

NCERT Solutions Mathematics Class 11 Chapter 13 - 8π(1)2

= π

4. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 9

Solution:

Given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 10

Substituting x = 4, we get

NCERT Solutions Mathematics Class 11 Chapter 13 - 11= [4(4) + 3] / (4 – 2)

= (16 + 3) / 2

= 19 / 2

5. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 12

Solution:

Given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 13

Substituting x = -1, we get

NCERT Solutions Mathematics Class 11 Chapter 13 - 14

= [(-1)10 + (-1)5 + 1] / (-1 – 1)

= (1 – 1 + 1) / – 2

= – 1 / 2

6. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 15

Solution:

Given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 16

= [(0 + 1)5 – 1] / 0

=0

Since, this limit is undefined

Substitute x + 1 = y, then x = y – 1

NCERT Solutions Mathematics Class 11 Chapter 13 - 17

7. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 18

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 19

8. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 20

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 21

9. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 22

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 23

= [a (0) + b] / c (0) + 1

= b / 1

= b

10. Evaluate the Given limit: NCERT Solutions Mathematics Class 11 Chapter 13 - 24

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 25

11. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 26

Solution:

Given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 27

Substituting x = 1

NCERT Solutions Mathematics Class 11 Chapter 13 - 28

= [a (1)2 + b (1) + c] / [c (1)2 + b (1) + a]

= (a + b + c) / (a + b + c)

Given

NCERT Solutions Mathematics Class 11 Chapter 13 - 29

= 1

12. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 30

Solution:

By substituting x = – 2, we get

NCERT Solutions Mathematics Class 11 Chapter 13 - 31

13. Evaluate the Given limit:NCERT Solutions Mathematics Class 11 Chapter 13 - 32

Solution:

Given NCERT Solutions Mathematics Class 11 Chapter 13 - 33

NCERT Solutions Mathematics Class 11 Chapter 13 - 34

14. Evaluate the given limit: NCERT Solutions Mathematics Class 11 Chapter 13 - 35

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 36

15. Evaluate the given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 37

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 38

16. Evaluate the given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 39

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 40

17. Evaluate the given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 41

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 42

NCERT Solutions Mathematics Class 11 Chapter 13 - 43

18. Evaluate the given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 44

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 45

19. Evaluate the given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 46

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 47

20. Evaluate the given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 48

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 49

NCERT Solutions Mathematics Class 11 Chapter 13 - 50

21. Evaluate the given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 51

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 52

NCERT Solutions Mathematics Class 11 Chapter 13 - 53

22. Evaluate the given limit:
NCERT Solutions Mathematics Class 11 Chapter 13 - 54

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 55

NCERT Solutions Mathematics Class 11 Chapter 13 - 56

23.
NCERT Solutions Mathematics Class 11 Chapter 13 - 57

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 58

NCERT Solutions Mathematics Class 11 Chapter 13 - 59

NCERT Solutions Mathematics Class 11 Chapter 13 - 60

24. Find
NCERT Solutions Mathematics Class 11 Chapter 13 - 61, where

NCERT Solutions Mathematics Class 11 Chapter 13 - 62

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 63

NCERT Solutions Mathematics Class 11 Chapter 13 - 64

25. Evaluate
NCERT Solutions Mathematics Class 11 Chapter 13 - 65, where f(x) =
NCERT Solutions Mathematics Class 11 Chapter 13 - 66

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 67

NCERT Solutions Mathematics Class 11 Chapter 13 - 68

NCERT Solutions Mathematics Class 11 Chapter 13 - 69

26. Find
NCERT Solutions Mathematics Class 11 Chapter 13 - 70, where f (x) =
NCERT Solutions Mathematics Class 11 Chapter 13 - 71

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 72

NCERT Solutions Mathematics Class 11 Chapter 13 - 73

27. Find
NCERT Solutions Mathematics Class 11 Chapter 13 - 74, where
NCERT Solutions Mathematics Class 11 Chapter 13 - 75

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 76

NCERT Solutions Mathematics Class 11 Chapter 13 - 77

28. Suppose
NCERT Solutions Mathematics Class 11 Chapter 13 - 78and if
NCERT Solutions Mathematics Class 11 Chapter 13 - 79what are possible values of a and b

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 80

NCERT Solutions Mathematics Class 11 Chapter 13 - 81

29. Let a1, a2,………an be fixed real numbers and define a function

f (x) = (x – a1) (x – a2) ……. (x – an).

What is
NCERT Solutions Mathematics Class 11 Chapter 13 - 82For some a ≠ a1, a2, ……. an, compute
NCERT Solutions Mathematics Class 11 Chapter 13 - 83

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 84

NCERT Solutions Mathematics Class 11 Chapter 13 - 85

30. If NCERT Solutions Mathematics Class 11 Chapter 13 - 86 For what value (s) of a does NCERT Solutions Mathematics Class 11 Chapter 13 - 87exists?

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 88

NCERT Solutions Mathematics Class 11 Chapter 13 - 89

NCERT Solutions Mathematics Class 11 Chapter 13 - 90

NCERT Solutions Mathematics Class 11 Chapter 13 - 91

31. If the function f(x) satisfies NCERT Solutions Mathematics Class 11 Chapter 13 - 92, evaluateNCERT Solutions Mathematics Class 11 Chapter 13 - 93

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 94

NCERT Solutions Mathematics Class 11 Chapter 13 - 95

32. If NCERT Solutions Mathematics Class 11 Chapter 13 - 96 For what integers m and n does both NCERT Solutions Mathematics Class 11 Chapter 13 - 97and NCERT Solutions Mathematics Class 11 Chapter 13 - 98exist?

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 99

NCERT Solutions Mathematics Class 11 Chapter 13 - 100

NCERT Solutions Mathematics Class 11 Chapter 13 - 101


Exercise 13.2 page no: 312

1. Find the derivative of x2– 2 at x = 10

Solution:

Let f (x) = x2 – 2

From first principle

NCERT Solutions Mathematics Class 11 Chapter 13 - 102

NCERT Solutions Mathematics Class 11 Chapter 13 - 103

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

Solution:

Let f (x) = x

Then,

NCERT Solutions Mathematics Class 11 Chapter 13 - 104

NCERT Solutions Mathematics Class 11 Chapter 13 - 105

3. Find the derivative of 99x at x = l00.

Solution:

Let f (x) = 99x,

From first principle

NCERT Solutions Mathematics Class 11 Chapter 13 - 106

= 99

4. Find the derivative of the following functions from first principle

(i) x3 – 27

(ii) (x – 1) (x – 2)

(iii) 1 / x2

(iv) x + 1 / x – 1

Solution:

(i) Let f (x) = x3 – 27

From first principle

NCERT Solutions Mathematics Class 11 Chapter 13 - 107

NCERT Solutions Mathematics Class 11 Chapter 13 - 108

(ii) Let f (x) = (x – 1) (x – 2)

From first principle

NCERT Solutions Mathematics Class 11 Chapter 13 - 109

NCERT Solutions Mathematics Class 11 Chapter 13 - 110

(iii) Let f (x) = 1 / x2

From first principle, we get

NCERT Solutions Mathematics Class 11 Chapter 13 - 111

NCERT Solutions Mathematics Class 11 Chapter 13 - 112

(iv) Let f (x) = x + 1 / x – 1

From first principle, we get

NCERT Solutions Mathematics Class 11 Chapter 13 - 113

NCERT Solutions Mathematics Class 11 Chapter 13 - 114

5. For the function NCERT Solutions Mathematics Class 11 Chapter 13 - 115 .Prove that f’ (1) =100 f’ (0).

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 116

NCERT Solutions Mathematics Class 11 Chapter 13 - 117

6. Find the derivative of NCERT Solutions Mathematics Class 11 Chapter 13 - 118 for some fixed real number a.

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 119

7. For some constants a and b, find the derivative of
(i) (x − a) (x − b)

(ii) (ax2 + b)2

(iii) x – a / x – b

Solution:

(i) (x – a) (x – b)

NCERT Solutions Mathematics Class 11 Chapter 13 - 120

(ii) (ax2 + b)2

NCERT Solutions Mathematics Class 11 Chapter 13 - 121

= 4ax (ax2 + b)

(iii) x – a / x – b

NCERT Solutions Mathematics Class 11 Chapter 13 - 122

NCERT Solutions Mathematics Class 11 Chapter 13 - 123

NCERT Solutions Mathematics Class 11 Chapter 13 - 124

8. Find the derivative of NCERT Solutions Mathematics Class 11 Chapter 13 - 125 for some constant a.

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 126

9. Find the derivative of

(i) 2x – 3 / 4

(ii) (5x3 + 3x – 1) (x – 1)

(iii) x-3 (5 + 3x)

(iv) x5 (3 – 6x-9)

(v) x-4 (3 – 4x-5)

(vi) (2 / x + 1) – x2 / 3x – 1

Solution:

(i)

NCERT Solutions Mathematics Class 11 Chapter 13 - 127

(ii)

NCERT Solutions Mathematics Class 11 Chapter 13 - 128

(iii)

NCERT Solutions Mathematics Class 11 Chapter 13 - 129

NCERT Solutions Mathematics Class 11 Chapter 13 - 130

(iv)

NCERT Solutions Mathematics Class 11 Chapter 13 - 131

(v)

NCERT Solutions Mathematics Class 11 Chapter 13 - 132

NCERT Solutions Mathematics Class 11 Chapter 13 - 133

(vi)

NCERT Solutions Mathematics Class 11 Chapter 13 - 134

NCERT Solutions Mathematics Class 11 Chapter 13 - 135

10. Find the derivative of cos x from first principle

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 136

NCERT Solutions Mathematics Class 11 Chapter 13 - 137

NCERT Solutions Mathematics Class 11 Chapter 13 - 138

NCERT Solutions Mathematics Class 11 Chapter 13 - 139

11. 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) 3 cot x + 5 cosec x

(vi) 5 sin x – 6 cos x + 7

(vii) 2 tan x – 7 sec x

Solution:

(i) sin x cos x

NCERT Solutions Mathematics Class 11 Chapter 13 - 140

NCERT Solutions Mathematics Class 11 Chapter 13 - 141

(ii) sec x

NCERT Solutions Mathematics Class 11 Chapter 13 - 142

NCERT Solutions Mathematics Class 11 Chapter 13 - 143

NCERT Solutions Mathematics Class 11 Chapter 13 - 144

(iii) 5 sec x + 4 cos x

NCERT Solutions Mathematics Class 11 Chapter 13 - 145

(iv) cosec x

NCERT Solutions Mathematics Class 11 Chapter 13 - 146

NCERT Solutions Mathematics Class 11 Chapter 13 - 147

NCERT Solutions Mathematics Class 11 Chapter 13 - 148

(v) 3 cot x + 5 cosec x

NCERT Solutions Mathematics Class 11 Chapter 13 - 149

NCERT Solutions Mathematics Class 11 Chapter 13 - 150

NCERT Solutions Mathematics Class 11 Chapter 13 - 151

NCERT Solutions Mathematics Class 11 Chapter 13 - 152

NCERT Solutions Mathematics Class 11 Chapter 13 - 153

NCERT Solutions Mathematics Class 11 Chapter 13 - 154

NCERT Solutions Mathematics Class 11 Chapter 13 - 155

NCERT Solutions Mathematics Class 11 Chapter 13 - 156

(vi)5 sin x – 6 cos x + 7

NCERT Solutions Mathematics Class 11 Chapter 13 - 157

NCERT Solutions Mathematics Class 11 Chapter 13 - 158

NCERT Solutions Mathematics Class 11 Chapter 13 - 159

(vii) 2 tan x – 7 sec x

NCERT Solutions Mathematics Class 11 Chapter 13 - 160

NCERT Solutions Mathematics Class 11 Chapter 13 - 161

NCERT Solutions Mathematics Class 11 Chapter 13 - 162

NCERT Solutions Mathematics Class 11 Chapter 13 - 163


Miscellaneous exercise page no: 317

1. Find the derivative of the following functions from first principle:

(i) –x 

(ii) (–x)–1 

(iii) sin (x + 1)

(iv) NCERT Solutions Mathematics Class 11 Chapter 13 - 164

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 165

(ii) (-x)-1

NCERT Solutions Mathematics Class 11 Chapter 13 - 166

NCERT Solutions Mathematics Class 11 Chapter 13 - 167

NCERT Solutions Mathematics Class 11 Chapter 13 - 168

NCERT Solutions Mathematics Class 11 Chapter 13 - 169

NCERT Solutions Mathematics Class 11 Chapter 13 - 170

= 1 / x2

(iii) sin (x + 1)

NCERT Solutions Mathematics Class 11 Chapter 13 - 171

NCERT Solutions Mathematics Class 11 Chapter 13 - 172

NCERT Solutions Mathematics Class 11 Chapter 13 - 173

(iv) NCERT Solutions Mathematics Class 11 Chapter 13 - 174

NCERT Solutions Mathematics Class 11 Chapter 13 - 175

We get,

NCERT Solutions Mathematics Class 11 Chapter 13 - 176

NCERT Solutions Mathematics Class 11 Chapter 13 - 177

NCERT Solutions Mathematics Class 11 Chapter 13 - 178

NCERT Solutions Mathematics Class 11 Chapter 13 - 179

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

2. (x + a)

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 180

3. (px + q) (r / x + s)

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 181

NCERT Solutions Mathematics Class 11 Chapter 13 - 182

NCERT Solutions Mathematics Class 11 Chapter 13 - 183

NCERT Solutions Mathematics Class 11 Chapter 13 - 184

4. (ax + b) (cx d)2

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 185

NCERT Solutions Mathematics Class 11 Chapter 13 - 186

5. (ax + b) / (cx + d)

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 187

NCERT Solutions Mathematics Class 11 Chapter 13 - 188

6. (1 + 1 / x) / (1 – 1 / x)

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 189

NCERT Solutions Mathematics Class 11 Chapter 13 - 190

NCERT Solutions Mathematics Class 11 Chapter 13 - 191

NCERT Solutions Mathematics Class 11 Chapter 13 - 192

7. 1 / (ax2 + bx + c)

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 193

NCERT Solutions Mathematics Class 11 Chapter 13 - 194

8. (ax + b) / px2 + qx + r

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 195

NCERT Solutions Mathematics Class 11 Chapter 13 - 196

NCERT Solutions Mathematics Class 11 Chapter 13 - 197

9. (px2 + qx + r) / ax + b

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 198

NCERT Solutions Mathematics Class 11 Chapter 13 - 199

10. (a / x4) – (b / x2) + cox x

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 200

NCERT Solutions Mathematics Class 11 Chapter 13 - 201

NCERT Solutions Mathematics Class 11 Chapter 13 - 202

11. NCERT Solutions Mathematics Class 11 Chapter 13 - 203

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 204

NCERT Solutions Mathematics Class 11 Chapter 13 - 205

12. (ax + b)n

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 206

NCERT Solutions Mathematics Class 11 Chapter 13 - 207

NCERT Solutions Mathematics Class 11 Chapter 13 - 208

NCERT Solutions Mathematics Class 11 Chapter 13 - 209

NCERT Solutions Mathematics Class 11 Chapter 13 - 210

NCERT Solutions Mathematics Class 11 Chapter 13 - 211

13. (ax + b)n (cx + d)m

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 212

NCERT Solutions Mathematics Class 11 Chapter 13 - 213

NCERT Solutions Mathematics Class 11 Chapter 13 - 214

NCERT Solutions Mathematics Class 11 Chapter 13 - 215

NCERT Solutions Mathematics Class 11 Chapter 13 - 216

14. sin (x + a)

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 217

NCERT Solutions Mathematics Class 11 Chapter 13 - 218

NCERT Solutions Mathematics Class 11 Chapter 13 - 219

NCERT Solutions Mathematics Class 11 Chapter 13 - 220

15. cosec x cot x

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 221

NCERT Solutions Mathematics Class 11 Chapter 13 - 222

So, we get

NCERT Solutions Mathematics Class 11 Chapter 13 - 223

NCERT Solutions Mathematics Class 11 Chapter 13 - 224

NCERT Solutions Mathematics Class 11 Chapter 13 - 225

NCERT Solutions Mathematics Class 11 Chapter 13 - 226

16. NCERT Solutions Mathematics Class 11 Chapter 13 - 227

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 228

NCERT Solutions Mathematics Class 11 Chapter 13 - 229

17.
NCERT Solutions Mathematics Class 11 Chapter 13 - 230

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 231

NCERT Solutions Mathematics Class 11 Chapter 13 - 232

NCERT Solutions Mathematics Class 11 Chapter 13 - 233

18.
NCERT Solutions Mathematics Class 11 Chapter 13 - 234

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 235

NCERT Solutions Mathematics Class 11 Chapter 13 - 236

NCERT Solutions Mathematics Class 11 Chapter 13 - 237

19. sinn x

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 238

NCERT Solutions Mathematics Class 11 Chapter 13 - 239

NCERT Solutions Mathematics Class 11 Chapter 13 - 240

NCERT Solutions Mathematics Class 11 Chapter 13 - 241

NCERT Solutions Mathematics Class 11 Chapter 13 - 242

20. NCERT Solutions Mathematics Class 11 Chapter 13 - 243

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 244

NCERT Solutions Mathematics Class 11 Chapter 13 - 245

21.
NCERT Solutions Mathematics Class 11 Chapter 13 - 246

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 247

NCERT Solutions Mathematics Class 11 Chapter 13 - 248

NCERT Solutions Mathematics Class 11 Chapter 13 - 249

NCERT Solutions Mathematics Class 11 Chapter 13 - 250

22. x4 (5 sin x – 3 cos x)

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 251

NCERT Solutions Mathematics Class 11 Chapter 13 - 252

23. (x2 + 1) cos x

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 253

24. (ax2 + sin x) (p + q cos x)

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 254

25. NCERT Solutions Mathematics Class 11 Chapter 13 - 255

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 256

NCERT Solutions Mathematics Class 11 Chapter 13 - 257

NCERT Solutions Mathematics Class 11 Chapter 13 - 258

26. NCERT Solutions Mathematics Class 11 Chapter 13 - 259

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 260

NCERT Solutions Mathematics Class 11 Chapter 13 - 261

27. NCERT Solutions Mathematics Class 11 Chapter 13 - 262

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 263

28. NCERT Solutions Mathematics Class 11 Chapter 13 - 264

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 265

NCERT Solutions Mathematics Class 11 Chapter 13 - 266

NCERT Solutions Mathematics Class 11 Chapter 13 - 267

NCERT Solutions Mathematics Class 11 Chapter 13 - 268

NCERT Solutions Mathematics Class 11 Chapter 13 - 269

29. (x + sec x) (x – tan x)

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 270

NCERT Solutions Mathematics Class 11 Chapter 13 - 271

NCERT Solutions Mathematics Class 11 Chapter 13 - 272

NCERT Solutions Mathematics Class 11 Chapter 13 - 273

NCERT Solutions Mathematics Class 11 Chapter 13 - 274

NCERT Solutions Mathematics Class 11 Chapter 13 - 275

NCERT Solutions Mathematics Class 11 Chapter 13 - 276

NCERT Solutions Mathematics Class 11 Chapter 13 - 277

NCERT Solutions Mathematics Class 11 Chapter 13 - 278

NCERT Solutions Mathematics Class 11 Chapter 13 - 279

NCERT Solutions Mathematics Class 11 Chapter 13 - 280

NCERT Solutions Mathematics Class 11 Chapter 13 - 281

30. NCERT Solutions Mathematics Class 11 Chapter 13 - 282

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 283

NCERT Solutions Mathematics Class 11 Chapter 13 - 284

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