{"id":4627,"date":"2016-05-17T11:49:00","date_gmt":"2016-05-17T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-13-1\/"},"modified":"2016-05-17T13:29:50","modified_gmt":"2016-05-17T07:59:50","slug":"ncert-solutions-class-11-maths-exercise-13-1","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-13-1\/","title":{"rendered":"NCERT Solutions class-11 Maths Exercise 13.1"},"content":{"rendered":"

Exercise 13.1<\/strong><\/p>\n

Evaluate the following limits in Exercises 1 to 22.<\/strong><\/p>\n

1. <\/strong><\/p>\n

Ans. <\/strong> 3 + 3 = 6<\/p>\n

\n

2. <\/strong><\/p>\n

Ans. <\/strong><\/p>\n

\n

3. <\/strong><\/p>\n

Ans. <\/strong><\/p>\n

\n

4. <\/strong><\/p>\n

Ans. <\/strong><\/p>\n

\n

5. <\/strong><\/p>\n

Ans. <\/strong><\/p>\n

\n

6. <\/strong><\/p>\n

Ans. <\/strong><\/p>\n

Putting as <\/p>\n

<\/p>\n

\n

7. <\/strong><\/p>\n

Ans. <\/strong><\/p>\n

= <\/p>\n

= <\/p>\n

\n

8. <\/strong><\/p>\n

Ans. <\/strong><\/p>\n

=<\/p>\n

= <\/p>\n

= <\/p>\n

\n

9. <\/strong><\/p>\n

Ans. <\/strong><\/p>\n

\n

10. <\/strong><\/p>\n

Ans. <\/strong><\/p>\n

= <\/p>\n

= <\/p>\n

= <\/p>\n

= = 1 + 1 = 2<\/p>\n

\n

11. <\/strong><\/p>\n

Ans. <\/strong><\/p>\n

= <\/p>\n

= = 1<\/p>\n

\n

12. <\/strong><\/p>\n

Ans. <\/strong> = <\/p>\n

= <\/p>\n

= = <\/p>\n

\n

13. <\/strong><\/p>\n

Ans. <\/strong><\/p>\n

= <\/p>\n

= = <\/p>\n

\n

14. <\/strong><\/p>\n

Ans. <\/strong><\/p>\n

= <\/p>\n

= <\/p>\n

= <\/p>\n

= <\/p>\n

\n

15. <\/strong><\/p>\n

Ans. <\/strong><\/p>\n

Putting as <\/p>\n

= <\/p>\n

= = <\/p>\n

= = <\/p>\n

\n

16. <\/strong><\/p>\n

Ans. <\/strong> = <\/p>\n

\n

17. <\/strong><\/p>\n

Ans. <\/strong> = <\/p>\n

= = <\/p>\n

= <\/p>\n

= = <\/p>\n

\n

18. <\/strong><\/p>\n

Ans. <\/strong><\/p>\n

= <\/p>\n

= <\/p>\n

= <\/p>\n

= <\/p>\n

\n

19. <\/strong><\/p>\n

Ans. <\/strong> = <\/p>\n

= = = 0<\/p>\n

\n

20. <\/strong><\/p>\n

Ans. <\/strong><\/p>\n

Dividing numerator and denominator by <\/p>\n

= <\/p>\n

= = = 1<\/p>\n

\n

21. <\/strong><\/p>\n

Ans. <\/strong>Given:<\/p>\n

= = <\/p>\n

= = <\/p>\n

= = 0<\/p>\n

\n

22. <\/strong><\/p>\n

Ans. <\/strong>Given:<\/p>\n

Putting as <\/p>\n

= = <\/p>\n

= = <\/p>\n

= <\/p>\n

\n

23. Find and where <\/strong><\/p>\n

Ans. <\/strong>Given:<\/p>\n

Now = <\/p>\n

And = 3 (1 + 1) = <\/p>\n

\n

24. Find where <\/strong><\/p>\n

Ans. <\/strong>Given:<\/p>\n

L.H.L.<\/p>\n

Putting as <\/p>\n

= <\/p>\n

= = 0<\/p>\n

R.H.L.<\/p>\n

Putting as <\/p>\n

= <\/p>\n

= = <\/p>\n

\n

25. Evaluate where <\/strong><\/p>\n

Ans. <\/strong>Given:<\/p>\n

L.H.L.<\/p>\n

Putting as <\/p>\n

= = = <\/p>\n

R.H.L.<\/p>\n

Putting as <\/p>\n

= = = <\/p>\n

Here, L.H.L. R.H.L.<\/p>\n

Therefore, this limit does not exist at <\/p>\n

\n

26. Find where <\/strong><\/p>\n

Ans. <\/strong>Given:<\/p>\n

L.H.L.<\/p>\n

Putting as <\/p>\n

= = = <\/p>\n

R.H.L.<\/p>\n

Putting as <\/p>\n

= = = <\/p>\n

Here, L.H.L. R.H.L.<\/p>\n

Therefore, this limit does not exist at <\/p>\n

\n

27. Find where <\/strong><\/p>\n

Ans. <\/strong>Given:<\/p>\n

L.H.L.<\/p>\n

Putting as <\/p>\n

= <\/p>\n

= = 0<\/p>\n

R.H.L.<\/p>\n

Putting as <\/p>\n

= <\/p>\n

= = 0<\/p>\n

Here, L.H.L. = R.H.L.<\/p>\n

Therefore, this limit exists at and <\/p>\n

\n

28. Suppose and if what are possible values of and ?<\/strong><\/p>\n

Ans. <\/strong>Given: and <\/p>\n

<\/p>\n

and\u2026\u2026\u2026 (i)<\/p>\n

Now<\/p>\n

Putting as <\/p>\n

<\/p>\n

= \u2026\u2026\u2026.(ii)<\/p>\n

Again<\/p>\n

Putting as <\/p>\n

<\/p>\n

= \u2026\u2026\u2026.(ii)<\/p>\n

Putting values from eq. (ii) and (iii) in eq. (i), we get<\/p>\n

and <\/p>\n

On solving these equation, we get and <\/p>\n

\n

29. Let be fixed real numbers and define a function What is ? For some compute <\/strong><\/p>\n

Ans. <\/strong>Given:<\/p>\n

Now<\/p>\n

= <\/p>\n

= = 0<\/p>\n

Also<\/p>\n

= <\/p>\n

\n

30. If for what values of does exists?<\/strong><\/p>\n

Ans. <\/strong>Given: <\/p>\n

exists for all <\/p>\n

Now L.H.L.<\/p>\n

Putting as <\/p>\n

= <\/p>\n

= = 0 + 1 = 1<\/p>\n

Also R.H.L.<\/p>\n

Putting as <\/p>\n

= <\/p>\n

= = <\/p>\n

Here, L.H.L. R.H.L.<\/p>\n

Therefore, this limit does not exist.<\/p>\n

\n

31. If the function satisfies valuate <\/strong><\/p>\n

Ans. <\/strong>Since<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

32. If for what integer and does both and exist?<\/strong><\/p>\n

Ans. <\/strong>Both and exist.<\/p>\n

and<\/p>\n

Now<\/p>\n

= = <\/p>\n

And<\/p>\n

= = <\/p>\n

<\/p>\n

\u2026\u2026\u2026.(i)<\/p>\n

Therefore, for exists we need <\/p>\n

Again<\/p>\n

= = <\/p>\n

And<\/p>\n

= <\/p>\n

= <\/p>\n

<\/p>\n

<\/p>\n

Therefore, exists for any integral value of and <\/p>\n","protected":false},"excerpt":{"rendered":"

Exercise 13.1 Evaluate the following limits in Exercises 1 to 22. 1. Ans. 3 + 3 = 6 2. Ans. 3. Ans. 4. Ans. 5. Ans. 6. Ans. Putting as 7. Ans. = = 8. Ans. = = = 9. Ans. 10. Ans. = = = = = 1 + 1 = 2 11. Ans. … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47,281],"tags":[],"class_list":["post-4627","post","type-post","status-publish","format-standard","hentry","category-cbse-class-11","category-ncert-solutions"],"yoast_head":"\nNCERT Solutions class-11 Maths Exercise 13.1 | myCBSEguide<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-13-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions class-11 Maths Exercise 13.1 | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"Exercise 13.1 Evaluate the following limits in Exercises 1 to 22. 1. Ans. 3 + 3 = 6 2. Ans. 3. Ans. 4. Ans. 5. Ans. 6. Ans. Putting as 7. Ans. = = 8. Ans. = = = 9. Ans. 10. Ans. = = = = = 1 + 1 = 2 11. Ans. ... 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