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Kunci Jawaban dan Pembahasan Soal || Buku Calculus 9th Purcell Chapter 1 - 1.5 Number 43 – 71

Pembahasan Soal Buku Calculus 9th Purcell Chapter 1 Section 1.1

CHAPTER 1 LIMITS

SECTION 1.5 Limits at Infinity; Infinite Limits


Problem Set 1.5, Number 43 – 71.

Calculus 9th Purcell Chapter 1 - 1.5

    In Problems 43-48, find the horizontal and vertical asymptotes for the graphs of the indicated functions. Then sketch their graphs.
  1. f(x) =
    3
    x + 1
    2. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5

    Calculus 9th Purcell Chapter 1 - 1.5


  2. f(x) =
    3
    (x + 1)2
    3. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5

    Calculus 9th Purcell Chapter 1 - 1.5


  3. F(x) =
    2x
    x – 3
    4. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5

    Calculus 9th Purcell Chapter 1 - 1.5


  4. F(x) =
    3
    9 – x2
    5. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5

    Calculus 9th Purcell Chapter 1 - 1.5


  5. g(x) =
    14
    2x2 + 7
    6. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5

    Calculus 9th Purcell Chapter 1 - 1.5


  6. g(x) =
    2x
    √(x2 + 5)
    7. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5

    Calculus 9th Purcell Chapter 1 - 1.5


  7. The line y = ax + b is called an oblique asymptote to the graph of y = f(x) if either
    8. lim
    [f(x) – (ax + b)]
    = 0
    x → ∞
     
     
    or
    lim
    [f(x) – (ax + b)]
    = 0
    x → –∞
     
     
    Find the oblique asymptote for
    f(x) =
    2x4 + 3x3 – 2x – 4
    x3 – 1
    Hint: Begin by dividing the denominator into the numerator.
    ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  8. Find the oblique asymptote for
    9. f(x) =
    3x3 + 4x2 – x + 1
    x2 + 1
    ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  9. Using the symbols M and δ, give precise definitions of each expression.
    10. (a)
    lim
    f(x) = – ∞
    x → c+
     
    (b)
    lim
    f(x) = ∞
    x → c-
     
    ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  10. Using the symbols M and N, give precise definitions of each expression.
    11. (a)
    lim
    f(x) = ∞
    x → ∞
     
    (b)
    lim
    f(x) = ∞
    x → –∞
     
    ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  11. Give a rigorous proof that if limx→∞ f(x) = A and limx→∞ g(x) = B, then
    12. lim
    [f(x) + g(x)] = A + B
    x → ∞
     
    ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


    Semoga Bermanfaat 😁

  12. We have given meaning to limx→A f(x) for A = a, a–, a+, –∞, ∞. Moreover, in each case, this limit may be L (finite), –∞, ∞, or may fail to exist in any sense. Make a table illustrating each of the 20 possible cases.
    13. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  13. Find each of the following limits or indicate that it does not exist even in the infinite sense.
    14. (a)
    lim
    sin x
    x → ∞
     
    (b)
    lim
    sin (1/x)
    x → ∞
     
    (c)
    lim
    x sin (1/x)
    x → ∞
     
    (d)
    lim
    x3/2 sin (1/x)
    x → ∞
     
    (e)
    lim
    x–1/2 sin x
    x → ∞
     
    (f)
    lim
    sin ([π/6] + [1/x])
    x → ∞
     
    (g)
    lim
    sin (x + [1/x])
    x → ∞
     
    (h)
    lim
    [sin (x + [1/x]) – sin x]
    x → ∞
     
    ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5

    Calculus 9th Purcell Chapter 1 - 1.5

    Calculus 9th Purcell Chapter 1 - 1.5

    Calculus 9th Purcell Chapter 1 - 1.5

    Calculus 9th Purcell Chapter 1 - 1.5

    Calculus 9th Purcell Chapter 1 - 1.5

    Calculus 9th Purcell Chapter 1 - 1.5

    Calculus 9th Purcell Chapter 1 - 1.5


  14. Einstein’s Special Theory of Relativity says that the mass m(v) of an object is related to its velocity v by
    15. m(v) =
    m0
    √1 – v2/c2
    Here m0 is the rest mass and c is the velocity of light. What is limv→c– m(v)?
    ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


    Semoga Bermanfaat 😁

    Use a computer or a graphing calculator to find the limits in Problems 57-64. Begin by plotting the function in an appropriate window.
  15. lim
    3x2 + x + 1
    x → ∞
    2x2 – 1
    16. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  16. lim
    √ (
    2x2 – 3x
    )
    x → –∞
    5x2 + 1
    17. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  17. lim
    [√(2x2 + 3x) – √(2x2 – 5)]
    x → –∞
     
    18. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  18. lim
    2x + 1
    x → ∞
    √(3x2 + 1)
    19. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  19. lim
     (
    1 +
    1
    )10
    x → ∞
    x
    20. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  20. lim
     (
    1 +
    1
    )x
    x → ∞
    x
    21. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  21. lim
     (
    1 +
    1
    )x2
    x → ∞
    x
    22. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  22. lim
     (
    1 +
    1
    )sin x
    x → ∞
    x
    23. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


    Find the one-sided limits in Problems 65-71. Begin by plotting the function in an appropriate window. Your computer may indicate that some of these limits do not exist, but, if so, you should be able to interpret the answer as either ∞ or –∞.
  23. lim
    sin |x – 3|
    x → 3–
    x – 3
    24. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  24. lim
    sin |x – 3|
    x → 3–
    tan (x – 3)
    25. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  25. lim
    cos (x – 3)
    x → 3–
    x – 3
    26. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  26. lim
    cos x
    x → (π/2)+
    x – π/2
    27. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  27. lim
    (1 + √x)1/√x
    x → 0+
     
    28. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  28. lim
    (1 + √x)1/x
    x → 0+
     
    29. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


  29. lim
    (1 + √x)x
    x → 0+
     
    30. ❤
    PEMBAHASAN:

    Calculus 9th Purcell Chapter 1 - 1.5


Semoga Bermanfaat 😁

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