NCERT Solutions for Class 11 Maths Chapter 13 Limits And Derivatives Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 13, contains solutions for all miscellaneous exercise questions. NCERT Solutions basically help in making students understand their strengths and weaknesses and provide an opportunity to improve their skills. It definitely boosts their confidence levels and help them to score well. The Miscellaneous Exercise of NCERT Solutions for Class 11 Maths Chapter 13- Limits and Derivatives is based on the following topics:

  1. Intuitive Idea of Derivatives
  2. Limits
  3. Limits of Trigonometric Functions
  4. Derivatives

Students can download NCERT Solutions of Class 11 maths from BYJU’S and practice them to prepare for the examination more effectively. The solutions provided here contain the answers to all the questions given in the NCERT textbook of Class 11.

Download PDF of NCERT Solutions for Class 11 Maths Chapter 13- Limits and Derivatives Miscellaneous Exercise

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Access Other Exercise Solutions of Class 11 Maths Chapter 13- Limits and Derivatives

Exercise 13.1 Solutions 32 Questions

Exercise 13.2 Solutions 11 Questions

Access NCERT Solutions for Class 11 Maths Chapter 13 Miscellaneous Exercise

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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