Matematika

Pertanyaan

1. lim x^2-x-6 / x^2-7x=12 jika x=9

2. lim 3x^2-8x+4 / x^2-5x+6 jika x=2

3. lim 2-√x / 4-x jika x=4

2 Jawaban

  • 1. 9² - 9 - 6 / 9² - 7(9) - 12
     66/6 = 11
    2. (3x - 2)(x - 2) / (x - 2)(x - 3)
          3x - 2 / x - 3
    x = 2
    3(2) - 2 / 2 - 3
    4 / -1
    = -4
    3. [tex] \frac{2 - \sqrt{x} }{4 - x} x \frac{2 + \sqrt{x} }{2 + \sqrt{x} } = \frac{(2 - \sqrt{x} )(2 + \sqrt{x})}{(4 - x)(2 + \sqrt{x} )} [/tex]
    = [tex] \frac{4 - x}{(4 - x)(2 + \sqrt{x} )} = \frac{1}{2 + \sqrt{x} } [/tex]
    x = 4
    = [tex] \frac{1}{2 + \sqrt{4} } = \frac{1}{2 + 2} = \frac{1}{4} [/tex]
  • 1. lim x^2-x-6 / x^2-7x+12
    = lim (x - 3)(x +2)/(x - 4)(x - 3) -------->> (coret "x - 3")
    = (x + 2)/(x - 4) ---------------------------->> (masukkan nilai "x = 9")
    = (9 + 2)/(9 - 4)
    = 11/5

    2). 
    lim 3x^2-8x+4 / x^2-5x+6
    = lim (3x - 2)(x - 2)/(x - 3)(x - 2) --------->> (coret "x - 2")
    = (3x - 2)/(x - 3) ------------------------------>> (masukkan nilai "x = 2")
    = (3.2 - 2)/(2 - 3)
    = (6 - 2)/-1
    = 4/-1
    = -4

    3). 
    lim 2-√x / 4-x
    = lim (2 - 
    √x)/(2 - √x)(2 + √x) ----------->> (coret "2 - √x")
    = 1/(2 + √x) --------------------------------->> (masukkan nilai "x = 4")
    = 1/(2 + √4)
    = 1/(2 + 2)
    = 1/4

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