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1          Ejercicios de límites Ficha ICalcula los siguientes límites                x2 5x + 2                           ...
x5 + a5                                                515. lim                                                           ...
p                3             x+6 2                                                                              132. lim...
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Ejercicios de limites 2º bach.ccss

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Ejercicios de limites 2º bach.ccss

  1. 1. 1 Ejercicios de límites Ficha ICalcula los siguientes límites x2 5x + 2 1 1. lim 2 1 x! 2 x + 3x 3 5 2x2 7x 4 2. lim 0 x!4 x3 + x2 10 x+2 3. lim +1 x!3+ x2 4x + 3 x+2 4. lim 1 x!3 x2 4x + 3 x+2 5. lim No existe (1 ) x!3 x2 4x + 3 x2 + 5 6. lim + 1:(2 ) x!3 x2 6x + 9 x+1 7. lim +1 x! 1 x3 + 3x2 + 3x + 1 x2 + 4x + 4 8. lim . No existe x! 2 x3 + 6x2 + 12x + 8 x + 4x + 4 = (x + 2)2 2 Ayuda: x + 6x2 + 12x + 8 = (x + 2)3 3 r r x3 2x + 5 26 9. lim x!3 4x2 x + 2 35 x2 25 10. lim 5 x!5 10 2x (x 1)(x 3)3 11. lim 0 x!3 (2x + 1)(2x 1)(x 3)2 x2 16 12. lim p 24 x!4 2x + 1 3 p x+1 2 1 p 13. lim p p 3 3 x!1 2x + 10 5x + 1 p x+1 2 2 14. lim p p x!3 2x + 10 5x + 1 3 1 x+2 x2 + 5 lim = +1 y lim 2 = 1 x!3+ x2 4x + 3 x!3 x 6x + 9 2 x2 6x + 9 = (x 3) 2 1
  2. 2. x5 + a5 515. lim a x! a x4 a4 4 (x + h)4 x416. lim 4x3 h!0 h x2 4 117. lim x!2 x3 2x2 + 4x 8 2 3 2 2x + 9x + 12x + 4 318. lim x! 2 3x3 + 11x2 + 8x 4 7 p x+4 2 119. lim x!0 x 4 p p x+h x 120. lim p h!0 h 2 x p3 r x2 1 6 421. lim p 6 x!1 x3 3x + 2 3 2x 1022. lim p 12 x!5 x + 4 3 x2 + 2x 823. lim 6 x!2 x3 6x2 + 11x 6 x2 x 124. lim x!0 5x2 + 3x 3 x3 4x2 + 4x 225. lim x!2 x3 3x2 + 4 3 x 1 x2 13x + 22 2 326. lim x!2 x2 8x + 12 2 px 13 127. lim x!3 x3 6 p x 6+x 528. lim x!3 x 3 6 x4 1 429. lim x! 1 x3 + 1 3 x2 + x 230. lim p 12 x!1 x + 3 2 2x 4 p31. lim x!3 ex 2 4 e 2
  3. 3. p 3 x+6 2 132. lim 12 x!2 x2 + 3x 2 0 Este límite presenta la indeterminación 0 p 3 A3 B 3 p 3 x+6 23 Ayuda: Como A B = 2 + AB + B 2 entonces: 3 x + 6 2 = p 2 p A 3 x+6 +23x+6+4 p p 3 3 x+6 2 3 x+6 23 lim = lim h p p i = x!2 x2 + 3x 2 2 x!2 3 x + 6 + 2 3 x + 6 + 4 ( x2 + 3x 2) x 2 lim h p 2 p i = x!2 3 3 x+6 + 2 x + 6 + 4 ( x + 1) (x 2) 1 1 1 lim h p 2 p i = (4+4+4)( 1) = 12 x!2 3 3 x+6 + 2 x + 6 + 4 ( x + 1) p 3 3x 2 + 233. lim x! 2 x2 + 3x + 10 0 Este límite presenta la indeterminación 0 p 3 A3 + B 3 p 3 3x 2 + 23 Al ser A+B = 2 2 entonces: 3 3x 2+2 = p 2 p A AB + B 3 3x 2 2 3 3x 2 +4 p p 3 3 3x 2 + 2 3 3x 2 + 23 lim = lim p p = x! 2 x2 + 3x + 10 x! 2 3 3x 2 2 3 2 3x 2 + 4 ( x2 + 3x + 10) 3 (x + 2) lim h p 2 p i = x! 2 3 3 3x 2 2 3x 2 + 4 (x + 2) ( x + 5) 3 3 1 lim h p 2 p i = (4+4+4)7 = 28 x! 2 3 3 3x 2 2 3x 2 + 4 ( x + 5) p x 1 3 134. lim 6 x!1 x2 + 1 p3 x+1 135. lim 6 x! 1 x2 + 1 p 5 7x 3 2 736. lim 800 x!5 x2 + 25 A5 B 5 Ayuda: A B= A4 + A3 B + A2 B 2 + AB 3 + B 4 p 5 3 7x + 3 + 237. lim x! 5 x2 + 253A A5 + B 5 +B = A4 A3 B + A2 B 2 AB 3 + B 4 3

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