Lim 2x-1/2x\xb2+3x-2, x>1\xf72, Lim x2074-4x\xb3-16/x\xb3-8, x>2, Lim 5x\xb3-40/x\xb2-4, x>2

19 sec read


Lim 2x-1/2x²+3x-2
x>1÷2
Lim x⁴-4x³-16/x³-8
x>2
Lim 5x³-40/x²-4
x>2​

Jawab:

1.    \frac{2}{5}

2. ∞

3. 0

Penjelasan dengan langkah-langkah:

1. lim         \frac{2x-1}{2x^{2} +3x-2}  

(x->1/2)

lim          \frac{(2x-1)}{(2x-1) (x+2)}

(x ->1/2)

karena nilai 2x-1 atas dengan yang bawah sama maka bisa kita coret menjadi

lim            \frac{1}{(x+2)}

(x->1/2)

setelah itu kita masukkan nilai x dari limit tersebut

lim          \frac{1}{\frac{1}{2} + 2 }    

(x->1/2)

lim        \frac{1}{\frac{5}{2} } / \frac{2}{5}

(x->1/2)

2. lim       \frac{\frac{x^{4} }{x^{3} }- \frac{4x^{3} }{x^{3} }-\frac{16}{x^{3} }  }{\frac{x^{3} }{x^{3} }-\frac{8}{x^{3} }   }  

   (x ->2)

lim          \frac{x-4-\frac{16}{x^{3} } }{1-\frac{8}{x^{3} } }

(x->2)

lim         \frac{-4}{1-\frac{8}{x^{3} } }

(x->2)

lim        \frac{-4}{0}

(x->2)

lim       ∞

(x->2)

3. lim       \frac{\frac{5x^{3} }{x^{2} }-\frac{40}{x^{2} }  }{\frac{x^{2} }{x^{2} }-\frac{4}{x^{2} }  }

   (x->2)

  lim       \frac{5x-\frac{40}{x^{2} } }{1-\frac{4}{x^{2} } }

  (x->2)

  lim       \frac{10-10}{1-1}

  (x->2)

  lim       0

  (x->2)


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