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Limits exercises for students, Exercises of Mathematics

Mathematics

42 limit exercises for students who want to practice and refresh their knowledge.Best for beginners Subject - Mathematics(Limits) Limits basics for beginners

Typology: Exercises

2024/2025

Available from 09/01/2025

isuru-sersinghe
isuru-sersinghe ๐Ÿ‡ฑ๐Ÿ‡ฐ

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Limits Exercises (1โ€“42)
1. lim
xโ†’0
x
sinโˆ’1x
2. lim
xโ†’0
sinโˆ’14x
x
3. lim
xโ†’0
sinโˆ’13x
sin x
4. lim
xโ†’โˆ’2
sinโˆ’1(x+ 2)
x2+ 2x
5. lim
xโ†’1/2
sinโˆ’1(2xโˆ’1)
4x2โˆ’1
6. lim
xโ†’3
tanโˆ’1(xโˆ’3)
x2โˆ’3x
7. lim
xโ†’โˆž
x2โˆ’6x
8. lim
xโ†’โˆž
7โˆ’3xโˆ’x3
9. lim
xโ†’โˆž
x2+ 6x+ 9
x+ 2
10. lim
xโ†’โˆž
x2+ 4x+ 9
x2+ 6x+ 13
11. lim
xโ†’โˆž
1โˆ’5xโˆ’x3
7xโˆ’7x3+ 1
12. lim
xโ†’โˆž
1
x2+ 3x+ 1
13. lim
xโ†’โˆž
x+ 3
x2+ 5x+ 1
14. lim
xโ†’โˆž
2x3+ 3x+ 1
x3+ 5x+ 1
15. lim
xโ†’โˆž
1โˆ’x3
x4+ 5x2+ 6
16. lim
xโ†’โˆž
2x3+ 3xโˆ’1
x2โˆ’2x+ 1
17. lim
xโ†’โˆž
โˆšx2+ 1 โˆ’x
x+ 1
1
pf3
pf4
pf5

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Download Limits exercises for students and more Exercises Mathematics in PDF only on Docsity!

Limits Exercises (1โ€“42)

  1. lim xโ†’ (^0) sin^ xโˆ’ (^1) x
  2. lim xโ†’ 0 sin

โˆ’ (^1 4) x x

  1. lim xโ†’ 0 sin

โˆ’ (^1 3) x sin x

  1. (^) xlimโ†’โˆ’ 2 sin

โˆ’ (^1) (x + 2) x^2 + 2x

  1. (^) xlimโ†’ 1 / 2 sin

โˆ’ (^1) (2x โˆ’ 1) 4 x^2 โˆ’ 1

  1. lim xโ†’ 3 tan โˆ’ (^1) (x โˆ’ 3) x^2 โˆ’ 3 x
  2. (^) xlimโ†’โˆž x^2 โˆ’ 6 x
  3. (^) xlimโ†’โˆž 7 โˆ’ 3 x โˆ’ x^3
  4. (^) xlimโ†’โˆž^ x

(^2) + 6x + 9 x + 2

  1. (^) xlimโ†’โˆž^ x

(^2) + 4x + 9 x^2 + 6x + 13

  1. (^) xlimโ†’โˆž^1 โˆ’^5 x^ โˆ’^ x 3 7 x โˆ’ 7 x^3 + 1
  2. (^) xlimโ†’โˆž x (^2) + 3^1 x + 1
  3. (^) xlimโ†’โˆž x (^2) + 5^ x^ + 3x + 1
  4. (^) xlimโ†’โˆž^2 x

(^3) + 3x + 1 x^3 + 5x + 1

  1. (^) xlimโ†’โˆž^1 โˆ’^ x 3 x^4 + 5x^2 + 6
  2. (^) xlimโ†’โˆž^2 x

(^3) + 3x โˆ’ 1 x^2 โˆ’ 2 x + 1

  1. (^) xlimโ†’โˆž

โˆšx (^2) + 1 โˆ’ x x + 1

  1. (^) xlimโ†’โˆž โˆš 4 x (^2) + 1^ x โˆ’ 1
  2. (^) xlimโ†’โˆž

โˆšx (^4) + 1 โˆ’ 2 x (^2) โˆ’ 1 x^2

  1. (^) xlimโ†’โˆž^ x (^2) โˆ’ x + 2 โˆšx (^4) + 2x + 3
  2. lim xโ†’ 0 e x (^) โˆ’ 1 x
  3. lim xโ†’ 0 e 5 x (^) โˆ’ 1 x
  4. lim xโ†’ (^0) e 3 x^7 xโˆ’ 1
  5. lim xโ†’ 0 e sin x (^) โˆ’ 1 sin x
  6. lim xโ†’ 0 e x (^) โˆ’ 1 sin x
  7. lim xโ†’ 0 e ax (^) โˆ’ ebx x
  8. lim xโ†’ 0 e 7 x (^) โˆ’ e 4 x sin x
  9. lim xโ†’ 05

x (^) โˆ’ 1 x

  1. lim xโ†’ 0 a

x (^) โˆ’ 1 x

  1. lim xโ†’ 0 a x (^) โˆ’ bx x
  2. lim xโ†’ 04 3 x (^) โˆ’ 1 x
  3. lim xโ†’ 0 xln^ โˆ’ x^1
  4. lim xโ†’ 1 sinx โˆ’^ ฯ€x 1
  5. lim xโ†’ 1

โˆš4 + x โˆ’ โˆš 6 โˆ’ x x^2 โˆ’ 1

  1. lim xโ†’ 2

p1 + โˆš2 + x โˆ’ โˆš 3 x โˆ’ 2

  1. ln a
    1. โˆ’
      1. a โˆ’ b
    1. ln
    1. 3 ln 30. ln a โˆ’ ln b
    1. 2 โˆš 33. โˆ’ฯ€
    1. 8 โˆš

Detailed Solution for Problem 41

x^ limโ†’ 045 xx^ โˆ’+ sin 3^ sin 2xx Step 1: Factor x in numerator and denominator: 4 x โˆ’ sin 2x 5 x + sin 3x =^

x 4 โˆ’ sin 2xx^  x 5 + sin 3xx^ ^ =

4 โˆ’ sin 2xx 5 + sin 3xx Step 2: Apply standard limits:

xlimโ†’ 0 sin 2x x= 2,^ xlimโ†’ 0 sin 3x x= 3 Step 3: Substitute and simplify:

xlimโ†’ 04 โˆ’^

sin 2xx 5 + sin 3xx^ =

Answer: (^14)