`lim_{x->oo} ( ((2x+2)(2x+1))/((x+1)(x+1)) )` ……………..

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1. Đáp án:`lim_{x->oo}(((2x+2)(2x+1))/((x+1)(x+1)))=4`

    

   Giải thích các bước giải:

   `lim_{x->oo}(((2x+2)(2x+1))/((x+1)(x+1)))`

   `=lim_{x->oo}((2(x+1)(2x+1))/((x+1)(x+1)))`

   `=lim_{x->oo}((2(2x+1))/(x+1))`

   `=lim_{x->oo}((4x+2)/(x+1))`

   `=lim_{x->oo}((4+2/x)/(1+1/x))`

   `=4/1=4`

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2. `lim_{x->oo} ( ((2x+2)(2x+1))/((x+1)(x+1)) )`

   `= lim_{x->oo} ((2x(1+2/(2x))(2x+1))/((x+1)(x+1)))`

   `= 2.lim_{x->oo} ( (x(1+2/(2x))(2x+1))/((x+1)(x+1)) )`

   `= 2 . lim_{x->oo} ( (2x+1)/(x+1) )`

   `= 2 . lim_{x->oo} ( (2+1/x)/(1+1/x) )`

   `= 2 . (lim_{x->oo}(2+1/x))/(lim_{x->oo}( 1 + 1/x))`

   `= 2 . 2/1`

   `= 4`

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